Gradient regularity in mixed local and nonlocal problems

DOI10.1007/s00208-022-02512-7arXiv2204.06590OpenAlexW4312123681MaRDI QIDQ6184761

Giuseppe Mingione, Cristiana De Filippis

Publication date: 29 January 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.06590

zbMATH Keywords

gradient regularity

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60) Fractional partial differential equations (35R11)

Related Items (6)

Variational methods for nonpositive mixed local-nonlocal operators ⋮ On a class of mixed local and nonlocal semilinear elliptic equation with singular nonlinearity ⋮ A Hölder estimate with an optimal tail for nonlocal parabolic \(p\)-Laplace equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
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• The second eigenvalue of the fractional \(p\)-Laplacian
• Local behavior of fractional \(p\)-minimizers
• Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case
• Nonlocal Harnack inequalities
• A nonlinear Stein theorem
• Hitchhiker's guide to the fractional Sobolev spaces
• Global Hölder regularity for the fractional \(p\)-Laplacian
• Hölder estimates for viscosity solutions of equations of fractional \(p\)-Laplace type
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Calderón-Zygmund estimates and non-uniformly elliptic operators
• Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
• Regularity in oscillatory nonlinear elliptic systems
• A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps
• Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part
• Differentiability of minima of non-differentiable functionals
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Regularity for minima of functionals with p-growth
• Regularity for a class of nonlinear elliptic systems
• Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
• The Dirichlet problem for the \(p\)-fractional Laplace equation
• Gagliardo-Nirenberg inequalities and non-inequalities: the full story
• Nonlinear Calderón-Zygmund theory in the limiting case
• Hölder regularity for nonlocal double phase equations
• Variational problems with long-range interaction
• Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case
• Maximizing the \(L^ \infty{}\) norm of the gradient of solutions to the Poisson equation
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications
• On the regularity of minima of non-autonomous functionals
• Manifold constrained non-uniformly elliptic problems
• A limiting problem for local/non-local \(p\)-Laplacians with concave-convex nonlinearities
• Interpolative gap bounds for nonautonomous integrals
• Regularity theory for mixed local and nonlocal parabolic \(p\)-Laplace equations
• Lipschitz bounds and nonautonomous integrals
• Self-improving inequalities for bounded weak solutions to nonlocal double phase equations
• Regularity for nonlocal problems with non-standard growth
• Hölder regularity for weak solutions to nonlocal double phase problems
• Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth
• Regularity estimates for fractional orthotropic \(p\)-Laplacians of mixed order
• Quasiconvexity and partial regularity via nonlinear potentials
• Interior and up to the boundary regularity for the fractional \(g\)-Laplacian: The convex case
• Fine boundary regularity for the degenerate fractional \(p\)-Laplacian
• Boundary Hölder regularity for elliptic equations
• Equivalence of solutions to fractional \(p\)-Laplace type equations
• Nonlocal self-improving properties
• Nonlocal equations with measure data
• Boundary regularity for almost minimizers of quasiconvex variational problems
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Linear and quasilinear elliptic equations
• The obstacle problem for nonlinear integro-differential operators
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations
• Boundary Harnack principle for $Δ+ Δ^{𝛼/2}$
• Maximal functions measuring smoothness
• Smoothness of Certain Degenerate Elliptic Equations
• Regularity of differential forms minimizing degenerate elliptic functionals.
• Differential Topology
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• Mixed local and nonlocal elliptic operators: regularity and maximum principles
• On the regularity theory for mixed local and nonlocal quasilinear elliptic equations
• Semilinear elliptic equations involving mixed local and nonlocal operators
• Guide to nonlinear potential estimates
• Nonlocal operators with singular anisotropic kernels
• On Weak and Viscosity Solutions of Nonlocal Double Phase Equations
• Local Hölder continuity for fractional nonlocal equations with general growth
• (Non)local logistic equations with Neumann conditions
• A Faber-Krahn inequality for mixed local and nonlocal operators
• The Wiener criterion for nonlocal Dirichlet problems

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