Calculus of Variations and Partial Differential Equations

Article	Citations
Existence results for double phase implicit obstacle problems involving multivalued operators	68
A mass supercritical problem revisited	60
Normalized solutions to the fractional Schrödinger equations with combined nonlinearities	45
Comparison methods for a Keller–Segel-type model of pattern formations with density-suppressed motilities	45
Normalized solutions for a Schrödinger equation with critical growth in $${\mathbb {R}}^{N}$$	38
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	27
New Examples on Lavrentiev Gap Using Fractals	25
The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications	24
Characterisation of homogeneous fractional Sobolev spaces	23
Multiple solutions of Kazdan–Warner equation on graphs in the negative case	22
The Calderón problem for the fractional Schrödinger equation with drift	21
Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism	20
Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy	20
Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation	20
Eventual smoothness and stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with rotational flux	20
Multiplicity results for (p, q)-Laplacian equations with critical exponent in $${\mathbb {R}}^N$$ and negative energy	20
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	19
On boundedness, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop	19
Optimal control of multiagent systems in the Wasserstein space	19
Existence of normalized ground states for the Sobolev critical Schrödinger equation with combined nonlinearities	18
Saddle solutions for the critical Choquard equation	17
A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type	17
On a planar non-autonomous Schrödinger–Poisson system involving exponential critical growth	17
Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems	17

Standing waves of the quintic NLS equation on the tadpole graph	17
Heat kernel on Ricci shrinkers	17
Local boundedness and Hölder continuity for the parabolic fractional p-Laplace equations	17
Non-uniqueness of weak solutions to hyperviscous Navier–Stokes equations: on sharpness of J.-L. Lions exponent	16
The fractional p-Laplacian evolution equation in $${\mathbb {R}}^N$$ in the sublinear case	15
$$\Gamma $$-convergence of polyconvex functionals involving s-fractional gradients to their local counterparts	15
Uniqueness of positive solutions with concentration for the Schrödinger–Newton problem	15
Limiting behavior and local uniqueness of normalized solutions for mass critical Kirchhoff equations	15
Asymptotic behavior of a quasilinear Keller–Segel system with signal-suppressed motility	14
A nonlocal isoperimetric problem with density perimeter	14
Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities	14
On global minimizers for a mass constrained problem	14
Higher integrability for variational integrals with non-standard growth	14
Mean field games with state constraints: from mild to pointwise solutions of the PDE system	14
Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality	14
A proof of the Caffarelli contraction theorem via entropic regularization	14
Excited states of Bose–Einstein condensates with degenerate attractive interactions	13
Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities	13
On one-dimension quasilinear wave equations with null conditions	13
A-priori gradient bound for elliptic systems under either slow or fast growth conditions	13
Jump processes as generalized gradient flows	13
On the planar Schrödinger equation with indefinite linear part and critical growth nonlinearity	13
Higher Hölder regularity for nonlocal equations with irregular kernel	12
Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka–Volterra competition model	12
A heat flow for the mean field equation on a finite graph	12
Entire solutions of time periodic bistable Lotka–Volterra competition-diffusion systems in $${\mathbb {R}}^N$$	12
Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in $${\mathbb {R}}^{1+3}$$	12
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	12
Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials	11
Korevaar–Schoen’s energy on strongly rectifiable spaces	11
Convex ancient solutions to curve shortening flow	11
Coupling local and nonlocal evolution equations	11
Curvature estimates for a class of Hessian type equations	11
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates	11
Global existence and convergence of a flow to Kazdan–Warner equation with non-negative prescribed function	11
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail	10
Sharp patterns of positive solutions for some weighted semilinear elliptic problems	10
The equilibrium measure for an anisotropic nonlocal energy	10
Regularity results for nonlocal equations and applications	10
Volume preserving mean curvature flow for star-shaped sets	10
Global higher integrability for minimisers of convex functionals with (p,q)-growth	10
On rectifiable measures in Carnot groups: representation	10
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	10
Relaxation of a scalar nonlocal variational problem with a double-well potential	10
Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum	10
The structure of the singular set in the thin obstacle problem for degenerate parabolic equations	10
Least energy solutions to a cooperative system of Schrödinger equations with prescribed $$L^2$$-bounds: at least $$L^2$$-critical growth	10
The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling	9
Stability of graphical tori with almost nonnegative scalar curvature	9
A mean curvature type flow with capillary boundary in a unit ball	9

Existence of varifold minimizers for the multiphase Canham–Helfrich functional	9
Geometric gradient estimates for fully nonlinear models with non-homogeneous degeneracy and applications	9
Bilinear embedding for divergence-form operators with complex coefficients on irregular domains	9
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	9
Regularity for parabolic equations with singular or degenerate coefficients	9
Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations	9
On the Brezis–Nirenberg problem for a Kirchhoff type equation in high dimension	9
Gradient estimates for multi-phase problems	9
Martin kernel of Schrödinger operators with singular potentials and applications to B.V.P. for linear elliptic equations	9
Ground states for the planar NLSE with a point defect as minimizers of the constrained energy	9
Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace–Beltrami operator	9
On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions	8
Lower semicontinuity and relaxation of nonlocal $$L^\infty $$-functionals	8
Index estimates for surfaces with constant mean curvature in 3-dimensional manifolds	8
Supercritical Moser–Trudinger inequalities and related elliptic problems	8
A coupled Schrödinger system with critical exponent	8
Blow-up solutions to the Monge–Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates	8
Fractional Sobolev metrics on spaces of immersions	8
Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates	8
Continuity and canceling operators of order n on $${\mathbb {R}}^n$$	8
Bounded solutions and their asymptotics for a doubly nonlinear Cahn–Hilliard system	8
Multi-marginal entropy-transport with repulsive cost	8
A theory of spectral partitions of metric graphs	8
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth	8
Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities	8
Local Hölder regularity for nonlocal equations with variable powers	8
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers	8
Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities	8
Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials	8
A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms	8
Elliptic quasi-variational inequalities under a smallness assumption: uniqueness, differential stability and optimal control	8
The $$L_p$$-Gaussian Minkowski problem	7
Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region	7
Large conformal metrics with prescribed Gaussian and geodesic curvatures	7
A combinatorial Yamabe problem on two and three dimensional manifolds	7
Classification of anti-symmetric solutions to nonlinear fractional Laplace equations	7
Uniqueness of the critical point for semi-stable solutions in $$\mathbb {R}^2$$	7
Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance	7
Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds	7
Gradient bounds for solutions to irregular parabolic equations with (p, q)-growth	7
Critical Stein–Weiss elliptic systems: symmetry, regularity and asymptotic properties of solutions	7
The Łojasiewicz–Simon inequality for the elastic flow	7
Nonlocal semilinear elliptic problems with singular nonlinearity	7
Existence of solutions to Chern–Simons–Higgs equations on graphs	7
Orlicz–Minkowski flows	7
Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunctions	7
Uniqueness of entire ground states for the fractional plasma problem	7
Flux & radii within the subconformal capacity	7
Best constants in Sobolev and Gagliardo–Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations	7
Capacity & perimeter from $$\alpha $$-Hermite bounded variation	7
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal	6
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	6
Liouville type results for semilinear biharmonic problems in exterior domains	6
Global solvability in a Keller-Segel-growth system with indirect signal production	6
Ground states of elliptic problems over cones	6
Inverse mean curvature evolution of entire graphs	6
Derivation of Darcy’s law in randomly perforated domains	6
On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary	6
Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold	6
Scattering for the non-radial inhomogenous biharmonic NLS equation	6
Solenoidal extensions in domains with obstacles: explicit bounds and applications to Navier–Stokes equations	6
Regularity for nonlocal problems with non-standard growth	6
Effects of corners in surface superconductivity	6
Existence and symmetry breaking of ground state solutions for Schrödinger–Poisson systems	6
Positive solutions of nonlinear elliptic equations involving supercritical Sobolev exponents without Ambrosetti and Rabinowitz condition	6
The Nirenberg problem on high dimensional half spheres: the effect of pinching conditions	6
On renormalized solutions to elliptic inclusions with nonstandard growth	6
Almost minimizers for the thin obstacle problem	6
Existence and uniqueness of bounded stable solutions to the Peierls–Nabarro model for curved dislocations	6
New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $$ {\mathbb {R}}^N $$ and applications	6
Traveling vortex pairs for 2D incompressible Euler equations	6
Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth	6
The sharp exponent in the study of the nonlocal Hénon equation in $${\mathbb {R}}^{N}$$: a Liouville theorem and an existence result	6
Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation	6
Some results on higher eigenvalue optimization	6
Semi-invariant Riemannian metrics in hydrodynamics	6
Geometry and interior nodal sets of Steklov eigenfunctions	5
Existence and nonexistence in the liquid drop model	5
Large scale Ricci curvature on graphs	5
G-invariant Szegő kernel asymptotics and CR reduction	5

Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data	5
Principal curves to nonlocal Lane–Emden systems and related maximum principles	5
Travelling helices and the vortex filament conjecture in the incompressible Euler equations	5
Local regularity for an anisotropic elliptic equation	5
A multi-material transport problem with arbitrary marginals	5
Exact number of single bubbling solutions for elliptic problems of Ambrosetti–Prodi type	5
Uniform $$W^{1,p}$$ estimates for an elliptic operator with Robin boundary condition in a $$\mathcal {C}^1$$ domain	5
The vanishing discount problem for monotone systems of Hamilton–Jacobi equations: part 2—nonlinear coupling	5
Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton–Jacobi equations	5
Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions	5
Nonlocal Harnack inequalities in the Heisenberg group	5
A fractional Hadamard formula and applications	5
On critical Kirchhoff problems driven by the fractional Laplacian	5
Some non-linear systems of PDEs related to inverse problems in conductivity	5
Multiple solutions for the Van der Waals–Allen–Cahn–Hilliard equation with a volume constraint	5
Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials	5
Noncoercive quasilinear elliptic operators with singular lower order terms	5
Natural second-order regularity for parabolic systems with operators having $$(p,\delta )$$-structure and depending only on the symmetric gradient	5
Pseudoconvexity for the special Lagrangian potential equation	5
A derivation of Griffith functionals from discrete finite-difference models	5
Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations	5
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	5
Geometry of log-concave functions: the $$L_p$$ Asplund sum and the $$L_{p}$$ Minkowski problem	5
Collapsing of the line bundle mean curvature flow on Kähler surfaces	5
Uniqueness and positivity issues in a quasilinear indefinite problem	5
The generalized porous medium equation on graphs: existence and uniqueness of solutions with $$\ell ^1$$ data	5
Hessian estimates for Lagrangian mean curvature equation	5
Linear stability estimates for Serrin’s problem via a modified implicit function theorem	5
Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions	5
Superharmonicity of curvature function for the convex level sets of harmonic functions	5
Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations	5
Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities	5
Regularity for the stationary Navier–Stokes equations over bumpy boundaries and a local wall law	5
Infinitely many positive solutions of nonlinear Schrödinger equations	5
Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour	5
The Lamm–Rivière system I: $$L^p$$ regularity theory	5
Global existence of smooth solution to relativistic membrane equation with large data	5
Representation formulas and pointwise properties for Barron functions	5
Uniqueness of the viscosity solution of a constrained Hamilton–Jacobi equation	5
Asymptotic expansions for singular solutions of $$\Delta u+e^u=0$$ in a punctured disc	4
Gradient estimates for singular parabolic p-Laplace type equations with measure data	4
On the constancy theorem for anisotropic energies through differential inclusions	4
Complete $$\lambda $$-surfaces in $${\mathbb {R}}^3$$	4
Spectral invariants of the perturbed polyharmonic Steklov problem	4
Radial single point rupture solutions for a general MEMS model	4
Stability of radially symmetric, monotone vorticities of 2D Euler equations	4
Hardy–Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs	4
A Rigidity Theorem for the deformed Hermitian-Yang-Mills equation	4
Small order asymptotics for nonlinear fractional problems	4
Solutions to Hamilton–Jacobi equation on a Wasserstein space	4
Local Lipschitz bounds for solutions to certain singular elliptic equations involving the one-Laplacian	4
A restricted nonlocal operator bridging together the Laplacian and the fractional Laplacian	4
One-dimensionality of the minimizers in the large volume limit for a diffuse interface attractive/repulsive model in general dimension	4
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials	4
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids	4
Uniform distribution of dislocations in Peierls–Nabarro models for semi-coherent interfaces	4
Convex hypersurfaces with prescribed scalar curvature and asymptotic boundary in hyperbolic space	4
Relaxation analysis in a data driven problem with a single outlier	4
Müller–Zhang truncation for general linear constraints with first or second order potential	4
Interior Hessian estimates for a class of Hessian type equations	4
A note on Newton’s problem of minimal resistance for convex bodies	4
Optimal measure transportation with respect to non-traditional costs	4
Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains	4
Global nonlinear stability of one kind of large solutions to evolutionary Faddeev model	4
Stability of smooth multi-solitons for the Camassa–Holm equation	4
Nonlinear nonlocal Douglas identity	4
The existence of embedded G-invariant minimal hypersurface	4
Sharp conditions for the linearization of finite elasticity	4
Non-uniqueness in law for the Boussinesq system forced by random noise	4
On the density of “wild” initial data for the compressible Euler system	4
Free boundary theory for singular/degenerate nonlinear equations with right hand side: a non-variational approach	4
The Euler–Helfrich functional	4
Riesz transforms of a general Ornstein–Uhlenbeck semigroup	4
Deformation of framed curves with boundary conditions	4
Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems	4
Improved regularity for the parabolic normalized p-Laplace equation	4
Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity	4
Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping	4
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces	4
Heat flow with Dirichlet boundary conditions via optimal transport and gluing of metric measure spaces	4
Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces	4
Optimal transport of vector measures	4
Mathematical validation of a continuum model for relaxation of interacting steps in crystal surfaces in 2 space dimensions	4
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	4
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	4
Global transversal stability of Euclidean planes under skew mean curvature flow evolutions	4
Upper and lower bounds for the Dunkl heat kernel	4
Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes	4
Convergence rate of general entropic optimal transport costs	4
Self-generating lower bounds and continuation for the Boltzmann equation	4
Coercivity estimates for integro-differential operators	4
Estimates of Dirichlet eigenvalues for degenerate $$\triangle _{\mu }$$-Laplace operator	4
Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation	4
Setting the Free Material Design problem through the methods of optimal mass distribution	4
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge–Ampère measures	4