Local regularity for nonlocal equations with variable exponents
From MaRDI portal
Publication:6073262
DOI10.1002/mana.202100521zbMath1525.35056arXiv2107.06043OpenAlexW4383273131MaRDI QIDQ6073262
Publication date: 17 October 2023
Published in: Mathematische Nachrichten (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.06043
weak solutionlocal boundednessHölder regularitynonlocal equationvariable exponentCaccioppoli estimatefractional Sobolev spaceDe Giorgi iteration
Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational methods applied to PDEs (35A15) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Integro-differential operators (47G20)
Related Items (1)
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
- Variable Lebesgue spaces. Foundations and harmonic analysis
- Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
- Lebesgue and Sobolev spaces with variable exponents
- Harnack's inequality for quasiminimizers with nonstandard growth conditions
- A priori estimates for integro-differential operators with measurable kernels
- Overview of differential equations with non-standard growth
- Function spaces of variable smoothness and integrability
- Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
- On Lavrentiev's phenomenon
- On some variational problems
- A transmission problem in the calculus of variations
- Hölder continuity of minimizers of functionals with variable growth exponent
- On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent
- Traces for fractional Sobolev spaces with variable exponents
- Comparison and sub-supersolution principles for the fractional \(p(x)\)-Laplacian
- Eigenvalue problems involving the fractional \(p(x)\)-Laplacian operator
- Harnack inequality for a class of functionals with non-standard growth via De Giorgi's method
- Relaxation of convex functionals: the gap problem
- Fractional De Giorgi classes and applications to nonlocal regularity theory
- The concentration-compactness principles for \(W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)\) and application
- Local Hölder regularity for nonlocal equations with variable powers
- On a class of fractional systems with nonstandard growth conditions
- General fractional Sobolev space with variable exponent and applications to nonlocal problems
- On optimal \(C^{1 , \alpha}\) estimates for \(p ( x )\)-Laplace type equations
- Existence and multiplicity of solutions for a Schrödinger-Kirchhoff type equation involving the fractional \(p(.,.)\)-Laplacian operator in \(\mathbb{R}^N\)
- Renormalized solutions for the fractional \(p(x)\)-Laplacian equation with \(L^1\) data
- Regularity estimates for elliptic nonlocal operators
- On a nonlocal fractional \(p\)(., .)-Laplacian problem with competing nonlinearities
- Density properties for fractional Sobolev spaces with variable exponents
- A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional \(p(\cdot)\)-Laplacian
- Nonlocal self-improving properties
- New regularity theorems for non-autonomous variational integrals with \((p,q)\)-growth
- Regularity and existence of solutions of elliptic equations with p,q- growth conditions
- Local Regularity for Parabolic Nonlocal Operators
- Regularity theory for parabolic nonlinear integral operators
- AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
- Hölder continuity of the gradient of p(x)-harmonic mappings
- A class of De Giorgi type and Hölder continuity
- Fractional Sobolev spaces with variable exponents and fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mrow> <mml:mo form="prefix">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math>-Laplacians
- Maximal function on generalized Lebesgue spaces L^p(⋅)
- Variable order nonlocal Choquard problem with variable exponents
- A critical Kirchhoff‐type problem driven by a p (·)‐fractional Laplace operator with variable s (·) ‐order
- Variable-order fractional Sobolev spaces and nonlinear elliptic equations with variable exponents
- Robin fractional problems with symmetric variable growth
- On a class of fractional p(x) -Kirchhoff type problems
- Regularity results for nonlocal parabolic equations
- Regularity results for a class of functionals with non-standard growth
- On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
This page was built for publication: Local regularity for nonlocal equations with variable exponents
