Calculus of Variations and Partial Differential Equations

Article	Citations
Existence results for double phase implicit obstacle problems involving multivalued operators	72
A mass supercritical problem revisited	68
Normalized solutions to the fractional Schrödinger equations with combined nonlinearities	49
Comparison methods for a Keller–Segel-type model of pattern formations with density-suppressed motilities	47
Normalized solutions for a Schrödinger equation with critical growth in $${\mathbb {R}}^{N}$$	45
Multiplicity and concentration of solutions to the nonlinear magnetic Schrödinger equation	30
On generalized Holmgren’s principle to the Lamé operator with applications to inverse elastic problems	29
New Examples on Lavrentiev Gap Using Fractals	26
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	26
Characterisation of homogeneous fractional Sobolev spaces	26
The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications	25
Multiple solutions of Kazdan–Warner equation on graphs in the negative case	24
Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation	23
Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy	23
Eventual smoothness and stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with rotational flux	22
Existence of normalized ground states for the Sobolev critical Schrödinger equation with combined nonlinearities	22
On boundedness, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop	20
Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism	20
Multiplicity results for (p, q)-Laplacian equations with critical exponent in $${\mathbb {R}}^N$$ and negative energy	20
Standing waves of the quintic NLS equation on the tadpole graph	19
Local boundedness and Hölder continuity for the parabolic fractional p-Laplace equations	19
Heat kernel on Ricci shrinkers	18
Limiting behavior and local uniqueness of normalized solutions for mass critical Kirchhoff equations	18
Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems	18
Saddle solutions for the critical Choquard equation	17

On a planar non-autonomous Schrödinger–Poisson system involving exponential critical growth	17
A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type	17
Mean field games with state constraints: from mild to pointwise solutions of the PDE system	16
On global minimizers for a mass constrained problem	16
Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities	16
Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality	16
Asymptotic behavior of a quasilinear Keller–Segel system with signal-suppressed motility	15
$$\Gamma $$-convergence of polyconvex functionals involving s-fractional gradients to their local counterparts	15
The fractional p-Laplacian evolution equation in $${\mathbb {R}}^N$$ in the sublinear case	15
A heat flow for the mean field equation on a finite graph	14
A nonlocal isoperimetric problem with density perimeter	14
Least energy solutions to a cooperative system of Schrödinger equations with prescribed $$L^2$$-bounds: at least $$L^2$$-critical growth	14
A proof of the Caffarelli contraction theorem via entropic regularization	14
Higher integrability for variational integrals with non-standard growth	14
Higher Hölder regularity for nonlocal equations with irregular kernel	13
Convex ancient solutions to curve shortening flow	13
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates	13
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	13
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail	13
Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials	13
Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in $${\mathbb {R}}^{1+3}$$	13
On the planar Schrödinger equation with indefinite linear part and critical growth nonlinearity	13
Entire solutions of time periodic bistable Lotka–Volterra competition-diffusion systems in $${\mathbb {R}}^N$$	13
On one-dimension quasilinear wave equations with null conditions	13
Excited states of Bose–Einstein condensates with degenerate attractive interactions	13
A-priori gradient bound for elliptic systems under either slow or fast growth conditions	13
Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities	13
Jump processes as generalized gradient flows	12
Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka–Volterra competition model	12
Curvature estimates for a class of Hessian type equations	12
Regularity results for nonlocal equations and applications	12
The equilibrium measure for an anisotropic nonlocal energy	11
Coupling local and nonlocal evolution equations	11
Global higher integrability for minimisers of convex functionals with (p,q)-growth	11
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	11
Global existence and convergence of a flow to Kazdan–Warner equation with non-negative prescribed function	11
The structure of the singular set in the thin obstacle problem for degenerate parabolic equations	11
Korevaar–Schoen’s energy on strongly rectifiable spaces	11
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	11
Ground states for the planar NLSE with a point defect as minimizers of the constrained energy	10
Existence of varifold minimizers for the multiphase Canham–Helfrich functional	10
On rectifiable measures in Carnot groups: representation	10
Martin kernel of Schrödinger operators with singular potentials and applications to B.V.P. for linear elliptic equations	10
Sharp patterns of positive solutions for some weighted semilinear elliptic problems	10
Regularity for parabolic equations with singular or degenerate coefficients	10
Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations	10
Local Hölder regularity for nonlocal equations with variable powers	10
Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates	10
Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum	9
A mean curvature type flow with capillary boundary in a unit ball	9

On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions	9
Best constants in Sobolev and Gagliardo–Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations	9
Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities	9
Gradient estimates for multi-phase problems	9
On the Brezis–Nirenberg problem for a Kirchhoff type equation in high dimension	9
Orlicz–Minkowski flows	9
Geometric gradient estimates for fully nonlinear models with non-homogeneous degeneracy and applications	9
Lower semicontinuity and relaxation of nonlocal $$L^\infty $$-functionals	9
Index estimates for surfaces with constant mean curvature in 3-dimensional manifolds	9
A theory of spectral partitions of metric graphs	9
Blow-up solutions to the Monge–Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates	9
Uniqueness of entire ground states for the fractional plasma problem	9
Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace–Beltrami operator	9
The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling	9
Bilinear embedding for divergence-form operators with complex coefficients on irregular domains	9
Stability of graphical tori with almost nonnegative scalar curvature	9
A coupled Schrödinger system with critical exponent	9
A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms	8
Gradient bounds for solutions to irregular parabolic equations with (p, q)-growth	8
Flux & radii within the subconformal capacity	8
Existence of solutions to Chern–Simons–Higgs equations on graphs	8
Regularity for nonlocal problems with non-standard growth	8
The $$L_p$$-Gaussian Minkowski problem	8
Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation	8
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers	8
Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials	8
Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities	8
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth	8
Critical Stein–Weiss elliptic systems: symmetry, regularity and asymptotic properties of solutions	8
Classification of anti-symmetric solutions to nonlinear fractional Laplace equations	8
A fractional Hadamard formula and applications	7
Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance	7
Noncoercive quasilinear elliptic operators with singular lower order terms	7
Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities	7
Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region	7
Some results on higher eigenvalue optimization	7
On renormalized solutions to elliptic inclusions with nonstandard growth	7
Uniqueness of the critical point for semi-stable solutions in $$\mathbb {R}^2$$	7
Capacity & perimeter from $$\alpha $$-Hermite bounded variation	7
Effects of corners in surface superconductivity	7
Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunctions	7
Existence and symmetry breaking of ground state solutions for Schrödinger–Poisson systems	7
The Łojasiewicz–Simon inequality for the elastic flow	7
A combinatorial Yamabe problem on two and three dimensional manifolds	7
Nonlocal semilinear elliptic problems with singular nonlinearity	7
Scattering for the non-radial inhomogenous biharmonic NLS equation	7
Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds	7
Positive solutions of nonlinear elliptic equations involving supercritical Sobolev exponents without Ambrosetti and Rabinowitz condition	7
Large conformal metrics with prescribed Gaussian and geodesic curvatures	7
On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary	7
Almost minimizers for the thin obstacle problem	7
Inverse mean curvature evolution of entire graphs	6
Derivation of Darcy’s law in randomly perforated domains	6
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal	6
Existence and uniqueness of bounded stable solutions to the Peierls–Nabarro model for curved dislocations	6
Solenoidal extensions in domains with obstacles: explicit bounds and applications to Navier–Stokes equations	6
G-invariant Szegő kernel asymptotics and CR reduction	6
Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials	6
Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth	6
Convergence rate of general entropic optimal transport costs	6
Asymptotic expansions for singular solutions of $$\Delta u+e^u=0$$ in a punctured disc	6
Small order asymptotics for nonlinear fractional problems	6
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	6
Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations	6
Traveling vortex pairs for 2D incompressible Euler equations	6
Optimal incompatible Korn–Maxwell–Sobolev inequalities in all dimensions	6
The sharp exponent in the study of the nonlocal Hénon equation in $${\mathbb {R}}^{N}$$: a Liouville theorem and an existence result	6
Self-generating lower bounds and continuation for the Boltzmann equation	6
Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold	6
The generalized porous medium equation on graphs: existence and uniqueness of solutions with $$\ell ^1$$ data	6
Existence and nonexistence in the liquid drop model	6
New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $$ {\mathbb {R}}^N $$ and applications	6
Solutions to Hamilton–Jacobi equation on a Wasserstein space	6
Ground states of elliptic problems over cones	6
The Nirenberg problem on high dimensional half spheres: the effect of pinching conditions	5
Hardy–Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs	5
Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces	5
Uniqueness of the viscosity solution of a constrained Hamilton–Jacobi equation	5
Geometry and interior nodal sets of Steklov eigenfunctions	5
To what extent is cross-diffusion controllable in a two-dimensional chemotaxis-(Navier–)Stokes system modeling coral fertilization	5

Non-uniqueness in law for the Boussinesq system forced by random noise	5
Sharp conditions for the linearization of finite elasticity	5
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs	5
Superharmonicity of curvature function for the convex level sets of harmonic functions	5
Nonlocal Harnack inequalities in the Heisenberg group	5
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	5
Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation	5
Local regularity for an anisotropic elliptic equation	5
Heat flow with Dirichlet boundary conditions via optimal transport and gluing of metric measure spaces	5
A multi-material transport problem with arbitrary marginals	5
Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations	5
Müller–Zhang truncation for general linear constraints with first or second order potential	5
Geometry of log-concave functions: the $$L_p$$ Asplund sum and the $$L_{p}$$ Minkowski problem	5
The Lamm–Rivière system I: $$L^p$$ regularity theory	5
The vanishing discount problem for monotone systems of Hamilton–Jacobi equations: part 2—nonlinear coupling	5
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	5
Representation formulas and pointwise properties for Barron functions	5
Global existence of smooth solution to relativistic membrane equation with large data	5
Natural second-order regularity for parabolic systems with operators having $$(p,\delta )$$-structure and depending only on the symmetric gradient	5
Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes	5
Upper and lower bounds for the Dunkl heat kernel	5
Hessian estimates for Lagrangian mean curvature equation	5
Principal curves to nonlocal Lane–Emden systems and related maximum principles	5
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials	5
Some non-linear systems of PDEs related to inverse problems in conductivity	5
Improved regularity for the parabolic normalized p-Laplace equation	5
Infinitely many positive solutions of nonlinear Schrödinger equations	5
Gradient estimates for singular parabolic p-Laplace type equations with measure data	5
Pseudoconvexity for the special Lagrangian potential equation	5
A derivation of Griffith functionals from discrete finite-difference models	5
Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems	5
Uniqueness and positivity issues in a quasilinear indefinite problem	5
Stability of smooth multi-solitons for the Camassa–Holm equation	5
Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions	5
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	5
Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton–Jacobi equations	5
Coercivity estimates for integro-differential operators	5
Linear stability estimates for Serrin’s problem via a modified implicit function theorem	5
On critical Kirchhoff problems driven by the fractional Laplacian	5
Global solvability in a Keller-Segel-growth system with indirect signal production	5
Large scale Ricci curvature on graphs	5
Travelling helices and the vortex filament conjecture in the incompressible Euler equations	5
Maximal metric surfaces and the Sobolev-to-Lipschitz property	5
Regularity for the stationary Navier–Stokes equations over bumpy boundaries and a local wall law	5
Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data	5
The effects of diffusion on the dynamics of a Lotka-Volterra predator-prey model with a protection zone	5
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge–Ampère measures	5
Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour	5
On the constancy theorem for anisotropic energies through differential inclusions	5
Collapsing of the line bundle mean curvature flow on Kähler surfaces	5
Sign-changing solutions for a modified nonlinear Schrödinger equation in $${\mathbb {R}}^N$$	4
An exterior overdetermined problem for Finsler N-Laplacian in convex cones	4
Estimates of Dirichlet eigenvalues for degenerate $$\triangle _{\mu }$$-Laplace operator	4
Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping	4
Setting the Free Material Design problem through the methods of optimal mass distribution	4
Interior Hessian estimates for a class of Hessian type equations	4
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	4
Uniform distribution of dislocations in Peierls–Nabarro models for semi-coherent interfaces	4
Uniform a priori estimates for solutions of higher critical order fractional equations	4
A note on Newton’s problem of minimal resistance for convex bodies	4
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	4
Mathematical validation of a continuum model for relaxation of interacting steps in crystal surfaces in 2 space dimensions	4
Optimal transport of vector measures	4
Global transversal stability of Euclidean planes under skew mean curvature flow evolutions	4
On torsional rigidity and ground-state energy of compact quantum graphs	4
The Euler–Helfrich functional	4
On subhomogeneous indefinite p-Laplace equations in the supercritical spectral interval	4
Upper bounds for the Steklov eigenvalues on trees	4
An isoperimetric problem with a competing nonlocal singular term	4
Relaxation analysis in a data driven problem with a single outlier	4
Convex hypersurfaces with prescribed scalar curvature and asymptotic boundary in hyperbolic space	4
Complete $$\lambda $$-surfaces in $${\mathbb {R}}^3$$	4
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces	4
Density of Lipschitz functions in energy	4
Spectral invariants of the perturbed polyharmonic Steklov problem	4
The existence of embedded G-invariant minimal hypersurface	4
Global nonlinear stability of one kind of large solutions to evolutionary Faddeev model	4
Sobolev estimates for fractional parabolic equations with space-time non-local operators	4
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	4
Riesz transforms of a general Ornstein–Uhlenbeck semigroup	4
Deformation of framed curves with boundary conditions	4
Bourgain–Brezis–Mironescu convergence via Triebel-Lizorkin spaces	4
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	4
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems	4
Global Existence, Regularity and Boundedness in a Higher-dimensional Chemotaxis-Navier-Stokes System with Nonlinear Diffusion and General Sensitivity	4
Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity	4
Optimal measure transportation with respect to non-traditional costs	4
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids	4
Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains	4
Global regularity for degenerate/singular parabolic equations involving measure data	4
Radial single point rupture solutions for a general MEMS model	4
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	4
Stability of radially symmetric, monotone vorticities of 2D Euler equations	4
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	4
Local Lipschitz bounds for solutions to certain singular elliptic equations involving the one-Laplacian	4