Calculus of Variations and Partial Differential Equations

Article	Citations
$$W^{\sigma ,p}$$ A priori estimates for fully nonlinear integro-differential equations	77
A new transportation distance with bulk/interface interactions and flux penalization	58
Uniqueness of conformal-harmonic maps on locally conformally flat 4-manifolds	36
Globally stable blowup profile for supercritical wave maps in all dimensions	36
Discrete infinity Laplace equations on graphs and tug-of-war games	36
A Liouville type result for fractional GJMS equations on higher dimensional spheres	35
Gradient estimates for parabolic nonlinear nonlocal equations	32
Dirichlet problem for degenerate Hessian quotient type curvature equations	32
Existence and orbital stability/instability of standing waves with prescribed mass for the $$L^{2}$$-supercritical NLS in bounded domains and exterior domains	30
Dynamics of nearly parallel vortex filaments for the Gross–Pitaevskii equation	28
Vanishing-concentration-compactness alternative for critical Sobolev embedding with a general integrand in $$\mathbb R^2$$	26
Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers	23
Existence of an optimal shape for the first eigenvalue of polyharmonic operators	22
Existence and asymptotic behaviors of solutions to Chern-Simons systems and equations on finite graphs	22
Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery	22
On the existence of closed $$C^{1,1}$$ curves of constant curvature	21
Global large solutions to a multi-dimensional compressible magnetohydrodynamic flows with a nonlinear initial constraint	21
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	21
Regularity of gradient vector fields giving rise to finite Caccioppoli partitions	20
Gauss curvature flow with an obstacle	19
A theory of spectral partitions of metric graphs	19
An exterior overdetermined problem for Finsler N-Laplacian in convex cones	18
Ground states of attractive Bose gases near the critical rotating velocity	18
Some conformally invariant gap theorems for Bach-flat 4-manifolds	18
Increase of mass and nonlocal effects in the homogenization of magneto-elastodynamics problems	18

A Bochner formula on path space for the Ricci flow	18
Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow	18
Homoclinics for singular strong force Lagrangian systems in $${\mathbb {R}}^N$$	17
Liouville results for semilinear integral equations with conical diffusion	16
Finite-time blow-up in fully parabolic quasilinear Keller–Segel systems with supercritical exponents	16
The obstacle problem for a higher order fractional Laplacian	16
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	16
Korevaar–Schoen’s energy on strongly rectifiable spaces	15
Multiple constant sign and nodal solutions for nonlinear nonhomogeneous elliptic equations depending on a parameter	15
On the weak Harnack estimate for nonlocal equations	15
Multiple solutions of the planar $$L_p$$ dual Minkowski problem	15
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	15
Non-polynomial entire solutions to Hessian equations	14
Convergence rates for linear elasticity systems on perforated domains	14
Gradient estimates for divergence form parabolic systems from composite materials	14
Absence of positive eigenvalues of magnetic Schrödinger operators	14
Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations	14
Two generalized Tricomi equations	14
Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas	14
Perturbative estimates for the one-phase Stefan problem	14
De Giorgi’s inequality for the thresholding scheme with arbitrary mobilities and surface tensions	13
Non-minimality of spirals in sub-Riemannian manifolds	13
On the lower bound of the principal eigenvalue of a nonlinear operator	13
Strict convexity and $$C^1$$ regularity of solutions to generated Jacobian equations in dimension two	13
Uniqueness for linear integro-differential equations in the real line and applications	13
Global existence of classical solutions for a reactive polymeric fluid near equilibrium	12
Compactness of certain class of singular minimal hypersurfaces	12
Upper bounds for the Steklov eigenvalues on trees	12
Nonexistence of solutions to quasilinear parabolic equations with a potential in bounded domains	12
Global vanishing viscosity limit for the two dimensional incompressible viscoelasticity in Lagrangian coordinates	12
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties	12
$$\displaystyle L^{\infty }$$-truncation of closed differential forms	11
A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity	11
Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping	11
Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions	11
Homogenization of the Allen–Cahn equation with periodic mobility	11
An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler–Lagrange equations related to general linear growth problems	11
Generalized Donaldson functionals and related nonlinear partial differential equations	11
Gradient estimates for singular parabolic p-Laplace type equations with measure data	11
A new class of discrete conformal structures on surfaces with boundary	11
Min–max minimal hypersurfaces with obstacle	10
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	10
Global Existence, Regularity and Boundedness in a Higher-dimensional Chemotaxis-Navier-Stokes System with Nonlinear Diffusion and General Sensitivity	10
Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen–Cahn	10
On the cauchy problem of 3D compressible, viscous, heat-conductive navier-stokes-Poisson equations subject to large and non-flat doping profile	10
Harnack inequality and principal eigentheory for general infinity Laplacian operators with gradient in $$\mathbb {R}^N$$ and applications	10
On the structure of minimizers of the Allen-Cahn energy for $$Z_N$$ symmetric nonnegative potentials with $$N+1$$ zeros	10
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge–Ampère measures	10
On $$W^{2,p}$$-estimates for solutions of obstacle problems for fully nonlinear elliptic equations with oblique boundary conditions	10
On the spectrum of a mixed-type operator with applications to rotating wave solutions	9

Asymptotic behavior of the eigenfrequencies of a thin elastic rod with non-uniform cross-section of extremely oblate shape	9
Critical functions and blow-up asymptotics for the fractional Brezis–Nirenberg problem in low dimension	9
Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy	9
On the prescribed scalar curvature problem with very degenerate prescribed functions	9
Stability estimates for the complex Monge-Ampère and Hessian equations	9
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	9
Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation	9
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	9
First and second derivative Hölder estimates for generated Jacobian equations	9
Fully non-linear elliptic equations on compact almost Hermitian manifolds	9
A variational setting for an indefinite Lagrangian with an affine Noether charge	9
Dimension reduction through gamma convergence for general prestrained thin elastic sheets	9
Improved regularity for the parabolic normalized p-Laplace equation	9
Convergence rate of hypersonic similarity for steady potential flows over two-dimensional Lipschitz wedge	9
Quasilinear Schrödinger equations with concave and convex nonlinearities	9
Existence of minimizers and convergence of critical points for a new Landau-de Gennes energy functional in nematic liquid crystals	9
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	8
Dichotomous concentrating solutions for a Schrödinger–Newton equation	8
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	8
Regularity theory for non-autonomous problems with a priori assumptions	8
Qualitative properties of nonnegative solutions of some semilinear elliptic equations in cylindrical domains	8
Optimization of total population in logistic model with nonlocal dispersals and heterogeneous environments	8
Optimal measure transportation with respect to non-traditional costs	8
Asymptotic behavior of least energy nodal solutions for biharmonic Lane–Emden problems in dimension four	8
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	8
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	8
On a multi-objective control problem for the Korteweg–de Vries equation	8
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	8
A continuum model for brittle nanowires derived from an atomistic description by $$\Gamma $$-convergence	8
The optimal Hölder exponent in Massari’s regularity theorem	8
Local uniqueness of ground states for the generalized Choquard equation	7
On a theorem by Schlenk	7
Monge–Ampère operators and valuations	7
Phase separation on varying surfaces and convergence of diffuse interface approximations	7
Hermitian Yang–Mills connections on pullback bundles	7
Geometry of generalized fluid flows	7
Schrödinger-poisson system with zero mass in $$\mathbb {R}^2$$ involving (2, q)-Laplacian: existence, asymptotic behavior and regularity of solutions	7
Isoperimetric inequalities and regularity of A-harmonic functions on surfaces	7
Regularity for quasi-minima of the Alt–Caffarelli functional	7
Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility	7
Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning	7
On the optimality and decay of p-Hardy weights on graphs	7
Local well-posedness of the 1d compressible Navier–Stokes system with rough data	7
An obstacle problem arising from American options pricing: regularity of solutions	7
Partial regularity for Lipschitz solutions to the minimal surface system	7
Generalized Brezis–Seeger–Van Schaftingen–Yung formulae and their applications in ball Banach Sobolev spaces	7
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	7
On the equilibrium shape of a crystal	7
On a novel gradient flow structure for the aggregation equation	7
A unified approach to self-improving property via K-functionals	7
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	7
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	7
Quantitative symmetry in a mixed Serrin-type problem for a constrained torsional rigidity	7
Nonlinear bound states with prescribed angular momentum	7
The well-posedness of incompressible rotational jet flows with gravity	7
Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory	7
Line-tension limits for line singularities and application to the mixed-growth case	6
Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance	6
Morse homology for the Hamiltonian action in cotangent bundles	6
Eventual smoothness and stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with rotational flux	6
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	6
Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials	6
Unbounded mass radial solutions for the Keller–Segel equation in the disk	6
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	6
Stability of quasi-entropy solutions of non-local scalar conservation laws	6
Optimal solutions for a class of set-valued evolution problems	6
Nonlinear scalar field $$(p_{1}, p_{2})$$-Laplacian equations in $$\mathbb {R}^{N}$$: existence and multiplicity	6
Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework	6
Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients	6
Conformal tori with almost non-negative scalar curvature	6
Homogenization of locally periodic parabolic operators with non-self-similar scales	6
Wolff potentials and measure data vectorial problems with Orlicz growth	6
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	6
Existence and dynamics of normalized solutions to nonlinear Schrödinger equations with mixed fractional Laplacians	6
Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems	6
The Petty projection inequality for sets of finite perimeter	6
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	6
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	6
Hessian estimates for the Lagrangian mean curvature flow	6
Correction to: “New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $${\mathbb {R}}^N $$ and applications”	6

$$\mathcal {A}$$-caloric approximation and partial regularity for parabolic systems with Orlicz growth	6
Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism	6
Remarks on semi-linear elliptic problem involving fractional Hardy operators	6
Interior Hessian estimates for a class of Hessian type equations	6
Energy identity and necklessness for $$\alpha $$-Dirac-harmonic maps into a sphere	6
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	6
Ground states of spin-1 BEC with attractive mean-field interaction trapped in harmonic potential in $${\mathbb {R}}^2$$	6
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	6
Weak KAM theory for action minimizing random walks	6
Geometric analysis of the Yang–Mills connections over compact Kähler surfaces	6
Characterization of symmetric polyconvexity in higher dimensions	6
Interior Hölder estimate for the linearized complex Monge–Ampère equation	6
Instability of Type (II) Lawson–Osserman cones	6
Hölder regularity for parabolic fractional p-Laplacian	5
Scalar and mean curvature comparison via $$\mu $$-bubbles	5
Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities	5
An obstacle problem for the p-elastic energy	5
An Intrinsic Harnack inequality for some non-homogeneous parabolic equations in non-divergence form	5
A fractional Hadamard formula and applications	5
Some elliptic problems involving the gradient on general bounded and exterior domains	5
Hessian estimates for Lagrangian mean curvature equation	5
Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups	5
Scattering for the non-radial inhomogenous biharmonic NLS equation	5
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $$N=4,5$$	5
Asymptotic behavior of the generalized principal eigenvalue for an inhomogeneous cooperative system with nonlocal dispersal	5
A flow approach to mean field equation	5
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	5
A nondegeneracy condition for a semilinear elliptic system and the existence of multibump solutions	5
Boundary layer problems for the two-dimensional inhomogeneous incompressible magnetohydrodynamics equations	5
Linear inverse problems with Hessian–Schatten total variation	5
Existence and decays of solutions for fractional Schrödinger equations with general potentials	5
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature	5
Gradient estimates for multi-phase problems	5
On critical Kirchhoff problems driven by the fractional Laplacian	5
An abstract critical point theorem with applications to elliptic problems with combined nonlinearities	5
Resolvent estimates for wave operators in Lipschitz domains	5
Boundary expansions of complete conformal metrics with negative Ricci curvatures	5
Optimal regularity of isoperimetric sets with Hölder densities	5
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	5
$$L^p$$-Hardy identities and inequalities with respect to the distance and mean distance to the boundary	5
Global wellposedness and asymptotic behavior of axisymmetric strong solutions to the vacuum free boundary problem of isentropic compressible Navier–Stokes equations	5
Convergence to the grim reaper for a curvature flow with unbounded boundary slopes	5
Existence of nontopological solutions of the self-dual Einstein-Maxwell-Higgs equations on compact surfaces	5
A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary	5
On n-superharmonic functions and some geometric applications	5
Regularity properties for quasiminimizers of a (p, q)-Dirichlet integral	5
Deformation of framed curves with boundary conditions	5
Existence and uniqueness of bounded stable solutions to the Peierls–Nabarro model for curved dislocations	5
Classification of finite Morse index solutions to the polyharmonic Hénon equation	5
On the Morse index of critical points in the viscosity method	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
Uniform a priori estimates for positive solutions of the Lane–Emden system in the plane	4
Prescribed mass standing waves for energy critical Hartree equations	4
Extensions and traces of BV functions in rough domains and generalized Cheeger sets	4
$$L^\infty $$-estimates in optimal transport for non quadratic costs	4
Non-occurrence of gap for one-dimensional non-autonomous functionals	4
The Euler–Helfrich functional	4
Trace inequalities of the Sobolev type and nonlinear Dirichlet problems	4
Classification of the spreading behaviors of a two-species diffusion-competition system with free boundaries	4
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	4
Semi-discrete optimal transport methods for the semi-geostrophic equations	4
Multiple high energy solutions for fractional Schrödinger equation with critical growth	4
Operator-norm homogenisation estimates for the system of Maxwell equations on periodic singular structures	4
Multiplicity of non-contractible closed geodesics on Finsler compact space forms	4
Solutions with various structures for semilinear equations in $$\mathbb R^n$$ driven by fractional Laplacian	4
Upper heat kernel estimates for nonlocal operators via Aronson’s method	4
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	4
Critical Hardy inequality on the half-space via the harmonic transplantation	4
Compactness for a class of integral functionals with interacting local and non-local terms	4
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	4
Nonlocal Harnack inequalities in the Heisenberg group	4
Apriori decay estimates for Hardy–Sobolev–Maz’ya equations	4
A Bernstein type result of translating solitons	4
Anisotropic surface tensions for phase transitions in periodic media	4
Boundary asymptotics of the relative Bergman kernel metric for curves	4
Free boundary regularity of the porous medium equation with nonlocal drifts in dimension one	4
Discrete Carleman estimates and three balls inequalities	4
Non-uniqueness in law for the Boussinesq system forced by random noise	4
Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities	4
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	4
The $$C^0$$-convergence at the Neumann boundary for Liouville equations	4
Two short closed geodesics on a sphere of odd dimension	4
Curvature estimates for stable minimal surfaces with a common free boundary	4
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	4
Elliptic methods for solving the linearized field equations of causal variational principles	4
A solution to Newton’s least resistance problem is uniquely defined by its singular set	4
Volume minimising unit vector fields on three dimensional space forms of positive curvature	4
Limit profiles for singularly perturbed Choquard equations with local repulsion	4
Gradient potential estimates in elliptic obstacle problems with Orlicz growth	4
Ricci flow does not preserve positive sectional curvature in dimension four	4
Curve-like concentration for Bose-Einstein condensates	4
Minimal measures on the level sets below Mañé critical value	4
Infinitely many solutions for elliptic equations with non-symmetric nonlinearities	4
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	4