Calculus of Variations and Partial Differential Equations

Article	Citations
The well-posedness of incompressible rotational jet flows with gravity	95
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	42
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	39
Characterization of symmetric polyconvexity in higher dimensions	37
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	36
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	29
On a multi-objective control problem for the Korteweg–de Vries equation	26
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	25
Conformal tori with almost non-negative scalar curvature	22
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	22
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	22
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	21
On the optimality and decay of p-Hardy weights on graphs	21
On a novel gradient flow structure for the aggregation equation	19
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	19
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	19
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	19
Comparison theorems on H-type sub-Riemannian manifolds	18
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	18
Dichotomous concentrating solutions for a Schrödinger–Newton equation	17
Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	17
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	17
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	17
Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	17
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	17

Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	17
Wolff potentials and measure data vectorial problems with Orlicz growth	16
Improved regularity for the parabolic normalized p-Laplace equation	16
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	15
Upper bounds for the Steklov eigenvalues on trees	15
Regularity theory for non-autonomous problems with a priori assumptions	15
Scattering for the non-radial inhomogenous biharmonic NLS equation	14
Compactness for a class of integral functionals with interacting local and non-local terms	14
Hölder regularity for parabolic fractional p-Laplacian	14
One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $$N=4,5$$	14
On the equilibrium shape of a crystal	14
An Intrinsic Harnack inequality for some non-homogeneous parabolic equations in non-divergence form	13
Minimisers of supremal functionals and mass-minimising 1-currents	13
Small order asymptotics for nonlinear fractional problems	13
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	13
On p-harmonic self-maps of spheres	13
A vectorial problem with thin free boundary	13
Local solvability of the Poisson equation for closed $$G_2$$-structures	12
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	12
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	12
The Euler–Helfrich functional	12
Free boundary CMC annuli in spherical and hyperbolic balls	12
Local boundedness for solutions of a class of nonlinear elliptic systems	12
Discrete Carleman estimates and three balls inequalities	12
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	11
Convergence of semi-convex functions in CAT(1)-spaces	11
On blow up for a class of radial Hartree type equations	11
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	11
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	11
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	11
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	11
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	11
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	11
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	10
Variational analysis of nonlocal Dirichlet problems in periodically perforated domains	10
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	10
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	10
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	10
Scalar and mean curvature comparison via $$\mu $$-bubbles	10
On the singular planar Plateau problem	10
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	10
Existence and nonexistence in the liquid drop model	10
Apriori decay estimates for Hardy–Sobolev–Maz’ya equations	10
Weighted fractional Poincaré inequalities via isoperimetric inequalities	10
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	9
Optimal coordinates for Ricci-flat conifolds	9
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	9
Boundary regularity of an isotropically censored nonlocal operator	9
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	9
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	9

Uniqueness of weak solutions of the Plateau flow	9
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	9
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	9
Hardy–Sobolev interpolation inequalities	9
Conformal Dirac–Einstein equations on manifolds with boundary.	9
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
The dual $$p$$-convex functions and its applications	8
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	8
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	8
Graphical mean curvature flow with bounded bi-Ricci curvature	8
The $$L_{p}$$ dual Christoffel-Minkowski problem for $$1<p<q\le k+1$$ with $$1\le k\le n$$	8
On evolutionary problems with a-priori bounded gradients	8
Phase transition of an anisotropic Ginzburg–Landau equation	8
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	8
On convex functions and elliptic operators	8
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	8
On rectifiable measures in Carnot groups: representation	8
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	8
Blow up solutions for Sinh-Gordon equation with residual mass	8
On the second Robin eigenvalue of the Laplacian	8
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	8
On potentials whose level sets are orbits	8
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal	8
Convergence of interfaces in boundary reactions	8
Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces	8
Continuity of s-minimal functions	8
A free boundary isometric embedding problem in the unit ball	7
Hardy and Rellich inequality on lattices	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	7
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	7
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
The equality cases in Steiner’s projection inequality	7
On the random G equation with nonzero divergence	7
Higher regularity for weak solutions to degenerate parabolic problems	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
The compressible Euler system with nonlocal pressure: global existence and relaxation	7
On nonlinear instability of liquid Lane–Emden stars	7
Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting	7
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	7
Prescribing the gauss curvature of convex bodies in hyperbolic space	7
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	7
Manifolds for which Huber’s Theorem holds	7
Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends	7
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	7
A universal variational framework for parabolic equations and systems	7
Stability of spectral partitions and the Dirichlet-to-Neumann map	6
Lusin approximation for functions of bounded variation	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
A Maupertuis-type principle in relativistic mechanics and applications	6
Periodic solution for Hamiltonian type systems with critical growth	6
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	6
On the free boundary problems for the ideal incompressible MHD equations	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	6
A strong form of the quantitative Wulff inequality for crystalline norms	6
Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six	6
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
A variational characterization of calibrated submanifolds	6
Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime	6
Homogenisation of dynamical optimal transport on periodic graphs	6
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	6
A class of fourth-order dispersive wave equations with exponential source	6
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	6
Prescribing discrete Gaussian curvature on polyhedral surfaces	6
Smooth approximation of mappings with rank of the derivative at most 1	6
Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations	6
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	6
On spin-2 Bose–Einstein condensates: classification and dynamic behavior of ground states	5

Dirichlet problem for degenerate Hessian quotient type curvature equations	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
The existence and stability of solutions for liquid crystal two-phase interface problems	5
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth	5
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	5
Regularity for nonlocal problems with non-standard growth	5
Infinitely many nodal solutions of Kirchhoff-type equations with asymptotically cubic nonlinearity without oddness hypothesis	5
Variational aspects of phase transitions with prescribed mean curvature	5
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature	5
Hessian estimates for the Lagrangian mean curvature flow	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	5
Transition fronts of combustion reaction–diffusion equations around an obstacle	5
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	5
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	5
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds	5
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	5
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	5
Rigidity of Finsler gradient steady Ricci soliton	5
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
The rigidity of weighted eigenvalues on manifolds with nonnegative Ricci curvature	5
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
Non-uniqueness in law for the Boussinesq system forced by random noise	5
Non-minimality of spirals in sub-Riemannian manifolds	5
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	5
Volume comparison theorem with respect to sigma-k curvature	5
Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework	5
Boundary plasmas for a confined plasma problem in dimensional two	5
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	5
The half-volume spectrum of a manifold	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
Volume minimising unit vector fields on three dimensional space forms of positive curvature	5
Sinh-Gordon equations on finite graphs	5
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	5
Existence and orbital stability/instability of standing waves with prescribed mass for the $$L^{2}$$-supercritical NLS in bounded domains and exterior domains	5
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
Second order necessary condition for a strong minimum in the classical problem of calculus of variations	4
A singular Kazdan–Warner problem on a compact Riemann surface	4
Stability of constrained solitary waves for the supercritical Kawahara equation	4
Characterisation of gradient flows for a given functional	4
Spectral invariants of the perturbed polyharmonic Steklov problem	4
Local uniqueness of blow-up solutions for critical Hartree equations in bounded domain	4
Fractional integration and optimal estimates for elliptic systems	4
Generalized gradient structures for measure-valued population dynamics and their large-population limit	4
Prescribed mass standing waves for energy critical Hartree equations	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
Multisolitons are the unique constrained minimizers of the KdV conserved quantities	4
Existence of solutions for a system with general Hardy–Sobolev singular criticalities	4
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	4
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings	4
On Lipschitz Geometry at infinity of complex analytic sets	4
Deformations of Q-curvature II	4
Entire solutions to the Swift–Hohenberg equation via a variational approach	4
Linear inverse problems with Hessian–Schatten total variation	4
A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation	4
The global curvature estimate for the $$n-2$$ Hessian equation	4
Approximation of partial differential equations on compact resistance spaces	4
Deformation of discrete conformal structures on surfaces	4
Foliation of area minimizing hypersurfaces in asymptotically flat manifolds and Schoen’s conjecture	4
Density of Lipschitz functions in energy	4
Sharp uncertainty principles on metric measure spaces	4
Representation formulas and pointwise properties for Barron functions	4
Dirichlet problem for Krylov type equation in conformal geometry	4
Global weak solutions in nonlinear 3D thermoelasticity	4
Notes on generalized special Lagrangian equation	4
Optimal $$C^\infty $$-approximation of functions with exponentially or sub-exponentially integrable derivative	4
Axisymmetric steady Navier–Stokes flows under suction	4
On a sharp inequality of Adimurthi–Druet type and extremal functions	4
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
Gelfand-type problems in random walk spaces	4
$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents	4
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Singular solutions to the $$\sigma _k$$-Yamabe equation with prescribed asymptotics	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
The Einstein-scalar field Lichnerowicz equations on graphs	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	4
Li–Yau inequalities for the Helfrich functional and applications	4
Upper heat kernel estimates for nonlocal operators via Aronson’s method	4
Exponential decay of the solutions to nonlinear Schrödinger systems	4
Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations	4
The structure of stable codimension one integral varifolds near classical cones of density $$Q+1/2$$	4
Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space	4
Higher differentiability and integrability for some nonlinear elliptic systems with growth coefficients in BMO	3
Asymptotic behavior of positive solutions to the Lane-Emden system in dimension two	3