A fractional Gehring lemma, with applications to nonlocal equations

DOI10.4171/RLM/683zbMath1325.35260OpenAlexW2038523161WikidataQ58880721 ScholiaQ58880721MaRDI QIDQ484642

Tuomo Kuusi, Giuseppe Mingione, Yannick Sire

Publication date: 7 January 2015

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rlm/683

zbMATH Keywords

non-local operatorselliptic equationsGehring lemmaself-improving properties

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Integro-partial differential equations (45K05) Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Integro-partial differential equations (35R09)

Related Items (14)

On fractional regularity methods for a class of nonlocal problems ⋮ Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case ⋮ Nonlinear commutators for the fractional \(p\)-Laplacian and applications ⋮ On a new class of fractional partial differential equations. II ⋮ Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations ⋮ Fractional Hardy equations with critical and supercritical exponents ⋮ Regularity for a fractional p-Laplace equation ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double-phase equations ⋮ Hölder estimates for viscosity solutions of equations of fractional \(p\)-Laplace type ⋮ Higher integrability result for nonlinear elliptic systems with conormal boundary conditions ⋮ Self-improving inequalities for bounded weak solutions to nonlocal double phase equations ⋮ Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements ⋮ Equivalence of solutions to fractional \(p\)-Laplace type equations

Cites Work

• Meyers inequality and strong stability for stable-like operators
• Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions
• Regularity theory for parabolic nonlinear integral operators
• Analytical foundations of the theory of quasiconformal mappings in R^n
• Higher integrability of the gradient of minimizers of functional with nonstandard growth conditions
• A Characterization of Potential Spaces

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