Calculus of Variations and Partial Differential Equations

Article	Citations
Regularity theory for non-autonomous problems with a priori assumptions	101
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	45
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	42
Characterization of symmetric polyconvexity in higher dimensions	40
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	39
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	33
On a multi-objective control problem for the Korteweg–de Vries equation	30
Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	26
Conformal tori with almost non-negative scalar curvature	26
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	25
On the equilibrium shape of a crystal	24
Comparison theorems on H-type sub-Riemannian manifolds	24
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	23
Wolff potentials and measure data vectorial problems with Orlicz growth	22
The well-posedness of incompressible rotational jet flows with gravity	21
Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	20
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	20
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	19
Kähler Soliton Surfaces Are Generically Toric	19
Improved regularity for the parabolic normalized p-Laplace equation	19
Upper bounds for the Steklov eigenvalues on trees	18
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	18
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	17
On a novel gradient flow structure for the aggregation equation	17
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	17

Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	17
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	17
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	17
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	17
Hölder regularity for parabolic fractional p-Laplacian	16
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	16
Local solvability of the Poisson equation for closed $$G_2$$-structures	15
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	15
Dichotomous concentrating solutions for a Schrödinger–Newton equation	15
On the optimality and decay of p-Hardy weights on graphs	15
Compactness for a class of integral functionals with interacting local and non-local terms	14
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	14
Local boundedness for solutions of a class of nonlinear elliptic systems	14
Scalar and mean curvature comparison via $$\mu $$-bubbles	14
Small order asymptotics for nonlinear fractional problems	14
Free boundary CMC annuli in spherical and hyperbolic balls	14
Weighted fractional Poincaré inequalities via isoperimetric inequalities	14
On the singular planar Plateau problem	13
Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs	13
Apriori decay estimates for Hardy–Sobolev–Maz’ya equations	13
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	13
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	12
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	12
A vectorial problem with thin free boundary	12
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	12
One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $$N=4,5$$	12
An Intrinsic Harnack inequality for some non-homogeneous parabolic equations in non-divergence form	12
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	12
On p-harmonic self-maps of spheres	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
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	11
Minimisers of supremal functionals and mass-minimising 1-currents	11
On functionals involving the p-capacity and the q-torsional rigidity	11
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	11
Scattering for the non-radial inhomogenous biharmonic NLS equation	11
Variational analysis of nonlocal Dirichlet problems in periodically perforated domains	11
On blow up for a class of radial Hartree type equations	11
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	11
Convergence of semi-convex functions in CAT(1)-spaces	11
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	11
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	11
The Riemannian hemisphere is almost calibrated in the injective hull of its boundary	10
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	10
Global well-posedness for the Keller–Segel–Navier–Stokes system with nonlinear boundary conditions	10
The Euler–Helfrich functional	10
Hamilton-Ivey estimates for gradient Ricci solitons	10
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	10
The $$L_{p}$$ dual Christoffel-Minkowski problem for $$1<p<q\le k+1$$ with $$1\le k\le n$$	10
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	10

Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	10
Optimal coordinates for Ricci-flat conifolds	10
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	10
On convex functions and elliptic operators	9
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	9
Boundary regularity of an isotropically censored nonlocal operator	9
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	9
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	9
Hardy–Sobolev interpolation inequalities	9
Symmetry of uniformly rotating solutions for the vortex-wave system	9
Uniqueness of weak solutions of the Plateau flow	9
Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces	9
Phase transition of an anisotropic Ginzburg–Landau equation	9
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	9
Graphical mean curvature flow with bounded bi-Ricci curvature	9
Conformal Dirac–Einstein equations on manifolds with boundary.	9
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	9
Convergence of interfaces in boundary reactions	9
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	9
Global dynamics of the toxicant-taxis model with Robin boundary conditions	9
On evolutionary problems with a-priori bounded gradients	8
Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces	8
Blow up solutions for Sinh-Gordon equation with residual mass	8
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	8
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
The dual $$p$$-convex functions and its applications	8
Singularity Formation for the Higher Dimensional Skyrme Model	8
On potentials whose level sets are orbits	8
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	8
Continuity of s-minimal functions	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
On rectifiable measures in Carnot groups: representation	8
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	8
On the second Robin eigenvalue of the Laplacian	8
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	8
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	8
Hardy and Rellich inequality on lattices	7
Lusin approximation for functions of bounded variation	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
A free boundary isometric embedding problem in the unit ball	7
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
Stationary p–harmonic maps approaching planar singular harmonic maps to the circle	7
The equality cases in Steiner’s projection inequality	7
Prescribing the gauss curvature of convex bodies in hyperbolic space	7
Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime	7
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting	7
Manifolds for which Huber’s Theorem holds	7
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	7
Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies	7
On the random G equation with nonzero divergence	7
Periodic solution for Hamiltonian type systems with critical growth	7
Higher regularity for weak solutions to degenerate parabolic problems	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	7
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	7
The compressible Euler system with nonlocal pressure: global existence and relaxation	7
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	7
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
Singular perturbations models in phase transitions for anisotropic higher-order materials	6
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	6
Liouville type properties for a class of weighted anisotropic elliptic equations	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
New applications of Hadamard-in-the-mean inequalities to incompressible variational problems	6
Smooth approximation of mappings with rank of the derivative at most 1	6
On nonlinear instability of liquid Lane–Emden stars	6
On the free boundary problems for the ideal incompressible MHD equations	6
Prescribing discrete Gaussian curvature on polyhedral surfaces	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6
The existence and stability of solutions for liquid crystal two-phase interface problems	6
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
Variational aspects of phase transitions with prescribed mean curvature	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	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
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	6

Stability of spectral partitions and the Dirichlet-to-Neumann map	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	6
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	6
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	6
Rigidity of Finsler gradient steady Ricci soliton	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
A variational characterization of calibrated submanifolds	6
Homogenisation of dynamical optimal transport on periodic graphs	6
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	6
Global solvability for a two-phase problem of inhomogeneous incompressible viscous fluids	5
The rigidity of weighted eigenvalues on manifolds with nonnegative Ricci curvature	5
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	5
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	5
Formation of shifted shocks for the 3D compressible Euler equations with damping	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	5
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature	5
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	5
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
Desingularization of vortices for the incompressible Euler equation on a sphere	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
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions	5
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
The stability of the Boltzmann equation with deformations	5
On spin-2 Bose–Einstein condensates: classification and dynamic behavior of ground states	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
Hessian estimates for the Lagrangian mean curvature flow	5
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	5
Dirichlet problem for degenerate Hessian quotient type curvature equations	5
A class of fourth-order dispersive wave equations with exponential source	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
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	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
Regularity for nonlocal problems with non-standard growth	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
Sinh-Gordon equations on finite graphs	5
Boundary plasmas for a confined plasma problem in dimensional two	5
On Lipschitz Geometry at infinity of complex analytic sets	5
Infinitely many nodal solutions of Kirchhoff-type equations with asymptotically cubic nonlinearity without oddness hypothesis	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
Stability of constrained solitary waves for the supercritical Kawahara equation	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
The global curvature estimate for the $$n-2$$ Hessian equation	4
Density of Lipschitz functions in energy	4
Local uniqueness of blow-up solutions for critical Hartree equations in bounded domain	4
The half-volume spectrum of a manifold	4
Deformations of Q-curvature II	4
Volume minimising unit vector fields on three dimensional space forms of positive curvature	4
The structure of stable codimension one integral varifolds near classical cones of density $$Q+1/2$$	4
Axisymmetric steady Navier–Stokes flows under suction	4
A singular Kazdan–Warner problem on a compact Riemann surface	4
Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents	4
Generalized gradient structures for measure-valued population dynamics and their large-population limit	4
Sharp uncertainty principles on metric measure spaces	4
Compactness and existence results of the prescribing fractional Q-curvature problem on $$\mathbb {S}^n$$	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
Li–Yau inequalities for the Helfrich functional and applications	4
Deformation of discrete conformal structures on surfaces	4
Existence of solutions for a system with general Hardy–Sobolev singular criticalities	4
Gelfand-type problems in random walk spaces	4
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings	4
Transition fronts of combustion reaction–diffusion equations around an obstacle	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
Spectral invariants of the perturbed polyharmonic Steklov problem	4
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth	4
$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation	4
Improved Sobolev inequalities on CR sphere	4
Approximation of partial differential equations on compact resistance spaces	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	4
Global weak solutions in nonlinear 3D thermoelasticity	4
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	4
Representation formulas and pointwise properties for Barron functions	4
Entire solutions to the Swift–Hohenberg equation via a variational approach	4
On a sharp inequality of Adimurthi–Druet type and extremal functions	4
Linear inverse problems with Hessian–Schatten total variation	4
Optimal $$C^\infty $$-approximation of functions with exponentially or sub-exponentially integrable derivative	4
Notes on generalized special Lagrangian equation	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation	4