Calculus of Variations and Partial Differential Equations

Article	Citations
Characterization of symmetric polyconvexity in higher dimensions	51
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	45
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	39
On polynomial solutions to the minimal surface equation	38
Dichotomous concentrating solutions for a Schrödinger–Newton equation	32
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	32
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	30
Improved regularity for the parabolic normalized p-Laplace equation	28
On the optimality and decay of p-Hardy weights on graphs	28
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	27
Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	27
Hölder regularity for parabolic fractional p-Laplacian	27
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	25
On a novel gradient flow structure for the aggregation equation	23
Regularity theory for non-autonomous problems with a priori assumptions	23
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	23
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	23
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	21
Kähler Soliton Surfaces Are Generically Toric	20
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	19
Wolff potentials and measure data vectorial problems with Orlicz growth	19
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	18
On Rabinowitz’s minimal period conjecture and subharmonic solutions for the wave equation on a disk	17
On the equilibrium shape of a crystal	17
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	17

Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	16
On a multi-objective control problem for the Korteweg–de Vries equation	16
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	16
Local solvability of the Poisson equation for closed $$G_2$$-structures	16
The well-posedness of incompressible rotational jet flows with gravity	16
Comparison theorems on H-type sub-Riemannian manifolds	16
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	16
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	15
On the Yamabe invariant of certain compact manifolds with boundary	15
Compactness for a class of integral functionals with interacting local and non-local terms	15
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	15
Scalar and mean curvature comparison via $$\mu $$-bubbles	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
A vectorial problem with thin free boundary	14
$$C^\alpha $$-well-posedness of first order degenerate differential equations in banach spaces	14
Variational analysis of nonlocal Dirichlet problems in periodically perforated domains	14
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	14
Weighted fractional Poincaré inequalities via isoperimetric inequalities	14
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	14
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	14
Variational structures for the Fokker–Planck equation with general Dirichlet boundary conditions	14
Hamilton-Ivey estimates for gradient Ricci solitons	13
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	13
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	13
Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs	13
Minimisers of supremal functionals and mass-minimising 1-currents	13
Convergence of semi-convex functions in CAT(1)-spaces	13
On the singular planar Plateau problem	13
The Riemannian hemisphere is almost calibrated in the injective hull of its boundary	13
On functionals involving the p-capacity and the q-torsional rigidity	13
On blow up for a class of radial Hartree type equations	13
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	13
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	12
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	12
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	12
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	12
Free boundary CMC annuli in spherical and hyperbolic balls	11
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	11
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	11
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	11
Scattering for the non-radial inhomogenous biharmonic NLS equation	11
Optimal coordinates for Ricci-flat conifolds	11
On p-harmonic self-maps of spheres	11
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	11
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	11
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	10
Boundary regularity of an isotropically censored nonlocal operator	10
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	10
Convergence of interfaces in boundary reactions	10
Hardy–Sobolev interpolation inequalities	10

Uniqueness of weak solutions of the Plateau flow	10
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	10
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	10
Phase transition of an anisotropic Ginzburg–Landau equation	10
Conformal Dirac–Einstein equations on manifolds with boundary.	10
Local minimizers in 3d of vector Allen-Cahn with a quadruple junction.	9
Global dynamics of the toxicant-taxis model with Robin boundary conditions	9
The dual $$p$$-convex functions and its applications	9
Symmetry of uniformly rotating solutions for the vortex-wave system	9
Some results on a gradient system with concave-convex and supercritical nonlinearities	9
Asymptotic expansions for conformal scalar curvature equations near isolated singularities	9
On potentials whose level sets are orbits	9
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	9
Blow up dynamics for the 3D energy-critical nonlinear Schrödinger equation	9
A Liouville property for eternal solutions to a supercritical semilinear heat equation	9
The $$L_{p}$$ dual Christoffel-Minkowski problem for $$1<p<q\le k+1$$ with $$1\le k\le n$$	9
Singularity Formation for the Higher Dimensional Skyrme Model	9
Graphical mean curvature flow with bounded bi-Ricci curvature	9
On evolutionary problems with a-priori bounded gradients	9
Best constants in subelliptic fractional Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups	9
Continuity of s-minimal functions	9
Global well-posedness for the Keller–Segel–Navier–Stokes system with nonlinear boundary conditions	9
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	9
Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces	9
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	9
Blow up solutions for Sinh-Gordon equation with residual mass	9
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	9
Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends	8
A universal variational framework for parabolic equations and systems	8
Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies	8
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	8
A multi-point maximum principle to prove global Harnack inequalities for Schrödinger operators	8
The equality cases in Steiner’s projection inequality	8
Hardy and Rellich inequality on lattices	8
On nonlinear instability of liquid Lane–Emden stars	8
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	8
The compressible Euler system with nonlocal pressure: global existence and relaxation	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
On the second Robin eigenvalue of the Laplacian	8
Stationary p–harmonic maps approaching planar singular harmonic maps to the circle	8
Topology of complete minimal submanifolds in $${\mathbb {R}}^{n+m}$$ with finite total curvature	8
On the random G equation with nonzero divergence	8
Higher regularity for weak solutions to degenerate parabolic problems	8
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	8
A Cheeger inequality for the drift Laplacian with Wentzell boundary condition	8
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	8
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	8
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	8
Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting	8
Prescribing the gauss curvature of convex bodies in hyperbolic space	8
On the free boundary problems for the ideal incompressible MHD equations	8
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	8
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	7
Smooth approximation of mappings with rank of the derivative at most 1	7
Homogenisation of dynamical optimal transport on periodic graphs	7
Stability of spectral partitions and the Dirichlet-to-Neumann map	7
New applications of Hadamard-in-the-mean inequalities to incompressible variational problems	7
Bifurcations in Lagrangian systems and geodesics I	7
Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition	7
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	7
A strong form of the quantitative Wulff inequality for crystalline norms	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
Symmetry breaking for local minimizers of a free discontinuity problem	7
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
Periodic solution for Hamiltonian type systems with critical growth	7
Lusin approximation for functions of bounded variation	7
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	7
$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	7
A variational characterization of calibrated submanifolds	7
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	7
Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime	7
Manifolds for which Huber’s Theorem holds	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
Prescribing negative curvature with cusps and conical singularities on compact surface	7
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
The existence and stability of solutions for liquid crystal two-phase interface problems	7
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	6
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	6
Regularity for nonlocal problems with non-standard growth	6

The stability of the Boltzmann equation with deformations	6
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	6
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	6
Rigidity of Finsler gradient steady Ricci soliton	6
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	6
Liouville type properties for a class of weighted anisotropic elliptic equations	6
A non-local approach to the generalized Stokes operator with bounded measurable coefficients	6
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	6
Thermo-elastodynamics of nonlinearly viscous solids	6
The rigidity of weighted eigenvalues on manifolds with nonnegative Ricci curvature	6
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
Dirichlet problem for degenerate Hessian quotient type curvature equations	6
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	6
Weighted isoperimetric ratios and extension problems for fractional conformal Laplacians	6
A class of fourth-order dispersive wave equations with exponential source	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	6
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
A Maupertuis-type principle in relativistic mechanics and applications	6
Hessian estimates for the Lagrangian mean curvature flow	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
Existence and orbital stability/instability of standing waves with prescribed mass for the $$L^{2}$$-supercritical NLS in bounded domains and exterior domains	6
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	6
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	6
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	6
The ultimate shape of solution to the $$\varvec{L_p}$$ Minkowski problem	6
Singular perturbations models in phase transitions for anisotropic higher-order materials	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	6
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
Sinh-Gordon equations on finite graphs	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	5
On spin-2 Bose–Einstein condensates: classification and dynamic behavior of ground states	5
Formation of shifted shocks for the 3D compressible Euler equations with damping	5
Uniqueness of Cylindrical Tangent Cones $$C_{p,q} \times \mathbb {R}$$	5
Multisolitons are the unique constrained minimizers of the KdV conserved quantities	5
Glued spaces and lower Ricci curvature bounds	5
Boundary plasmas for a confined plasma problem in dimensional two	5
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	5
Infinite-dimensional Lipschitz stability in the Calderón problem and general Zernike bases	5
A constant rank theorem for the Yamabe-type equations on locally conformally flat manifolds	5
Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
Global solvability for a two-phase problem of inhomogeneous incompressible viscous fluids	5
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	5
Blow-up and global existence for semilinear parabolic equations on infinite graphs	5
Upper heat kernel estimates for nonlocal operators via Aronson’s method	5
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
A variational perspective on the Generalized Snell’s Law and applications to liquid crystal optics	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	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
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
Desingularization of vortices for the incompressible Euler equation on a sphere	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
From almost smooth spaces to RCD spaces	5
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds	5
On Lipschitz Geometry at infinity of complex analytic sets	5
Local uniqueness of blow-up solutions for critical Hartree equations in bounded domain	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
Optimal $$C^\infty $$-approximation of functions with exponentially or sub-exponentially integrable derivative	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
Yamabe flow and locally conformally flat manifolds with positive pinched Ricci curvature	4
Improved Sobolev inequalities on CR sphere	4
Dirichlet problem for Krylov type equation in conformal geometry	4
Generalized gradient structures for measure-valued population dynamics and their large-population limit	4
Global weak solutions in nonlinear 3D thermoelasticity	4
A singular Kazdan–Warner problem on a compact Riemann surface	4
The global curvature estimate for the $$n-2$$ Hessian equation	4
Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
The limiting weak type behaviors for rough operators with $$L\log L({\mathbb {S}^{n-1}})$$ kernels, and characterizations	4
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation	4
Thurston’s sphere packings on 3-dimensional manifolds, I	4
The structure of stable codimension one integral varifolds near classical cones of density $$Q+1/2$$	4
Foliation of area minimizing hypersurfaces in asymptotically flat manifolds and Schoen’s conjecture	4
Existence and exponential stability of the global large strong solution to the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity and large velocity	4
Uniqueness of hyperbolic Busemann functions in the Newtonian N-body problem	4
Deformation of discrete conformal structures on surfaces	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
Density of Lipschitz functions in energy	4
The Einstein-scalar field Lichnerowicz equations on graphs	4
Spectral invariants of the perturbed polyharmonic Steklov problem	4
Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric	4
Compactness and existence results of the prescribing fractional Q-curvature problem on $$\mathbb {S}^n$$	4
Exponential decay of the solutions to nonlinear Schrödinger systems	4
Fractional integration and optimal estimates for elliptic systems	4
Stability of constrained solitary waves for the supercritical Kawahara equation	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Li–Yau inequalities for the Helfrich functional and applications	4