Open AccessSelf-Improving inequalities for bounded weak solutions to nonlocal double phase equations
Author(s) -
James M. Scott,
Tadele Mengesha
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021174
Subject(s) - bounded function , sobolev space , mathematics , differentiable function , nonlinear system , mathematical analysis , lemma (botany) , pure mathematics , operator (biology) , physics , quantum mechanics , ecology , biochemistry , chemistry , poaceae , repressor , gene , transcription factor , biology
We prove higher Sobolev regularity for bounded weak solutions to a class of nonlinear nonlocal integro-differential equations. The leading operator exhibits nonuniform growth, switching between two different fractional elliptic "phases" that are determined by the zero set of a modulating coefficient. Solutions are shown to improve both in integrability and differentiability. These results apply to operators with rough kernels and modulating coefficients. To obtain these results we adapt a particular fractional version of the Gehring lemma developed by Kuusi, Mingione, and Sire in their work "Nonlocal self-improving properties" Analysis & PDE , 8(1):57–114 for the specific nonlinear setting under investigation in this manuscript.