Global regularity results for non-homogeneous growth fractional problems

DOI10.1007/S12220-021-00837-4zbMath1485.35192arXiv2106.02501OpenAlexW3169636558MaRDI QIDQ2074489

Deepak Kumar, Jacques Giacomoni, Konijeti Sreenadh

Publication date: 10 February 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.02501

zbMATH Keywords

Harnack inequalityfractional \((p, q)\)-Laplacianinterior and boundary Hölder continuity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Fractional partial differential equations (35R11)

Related Items (11)

Fractional non-linear regularity, potential and balayage ⋮ A note on the global regularity results for strongly nonhomogeneous \(p,q\)-fractional problems and applications ⋮ Multiplicity and concentration of positive solutions for fractional unbalanced double-phase problems ⋮ Fractional \((p, q)\)-Schrödinger equations with critical and supercritical growth ⋮ Harnack inequality for nonlocal problems with non-standard growth ⋮ Harnack inequality for the nonlocal equations with general growth ⋮ A Choquard type equation involving mixed local and nonlocal operators ⋮ Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities ⋮ A strong maximum principle for mixed local and nonlocal p-Laplace equations ⋮ A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators ⋮ Eigenvalue for a problem involving the fractional \((p, q)\)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The second eigenvalue of the fractional \(p\)-Laplacian
• Local behavior of fractional \(p\)-minimizers
• Nonlocal Harnack inequalities
• Hitchhiker's guide to the fractional Sobolev spaces
• Convexity properties of Dirichlet integrals and Picone-type inequalities
• Global Hölder regularity for the fractional \(p\)-Laplacian
• Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
• A Hopf's lemma and a strong minimum principle for the fractional \(p\)-Laplacian
• Regularity results for nonlocal equations by approximation
• Some recent results on the Dirichlet problem for \((p,q)\)-Laplace equations
• Hölder regularity for nonlocal double phase equations
• On a fractional \(p \& q\) Laplacian problem with critical Sobolev-Hardy exponents
• Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case
• Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications
• Multiplicity results for \((p,q)\) fractional elliptic equations involving critical nonlinearities
• Multiplicity of positive solutions for a fractional \(p\& q\)-Laplacian problem in \(\mathbb{R}^N\)
• Recent developments in problems with nonstandard growth and nonuniform ellipticity
• Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems
• Fine boundary regularity for the degenerate fractional \(p\)-Laplacian
• Fractional \(p \& q\) Laplacian problems in \(\mathbb{R}^N\) with critical growth
• Fractional double-phase patterns: concentration and multiplicity of solutions
• Regularity estimates for elliptic nonlocal operators
• Equivalence of solutions to fractional \(p\)-Laplace type equations
• Nonlocal equations with measure data
• Existence, multiplicity and concentration for a class of fractional \( p \& q \) Laplacian problems in \( \mathbb{R} ^{N} \)
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• The obstacle problem for nonlinear integro-differential operators
• Boundary regularity for solutions of degenerate elliptic equations
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• Regularity and multiplicity results for fractional (p,q)-Laplacian equations
• Semilinear elliptic equations involving mixed local and nonlocal operators
• On harnack type inequalities and their application to quasilinear elliptic equations

This page was built for publication: Global regularity results for non-homogeneous growth fractional problems