On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems

Prashanta Garain, Wontae Kim, Juha Kinnunen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We establish existence results for a class of mixed anisotropic and nonlocal p-Laplace equations with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To this end, we also discuss the necessary regularity properties of weak solutions of the associated non-singular problems. More precisely, we obtain local boundedness of subsolutions, the Harnack inequality for solutions and the weak Harnack inequality for supersolutions.

Original languageEnglish
JournalFORUM MATHEMATICUM
DOIs
Publication statusE-pub ahead of print - 27 Oct 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • Mixed anisotropic and nonlocal p-Laplace equation, existence, regularity, singular problem, variable exponent

Fingerprint

Dive into the research topics of 'On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems'. Together they form a unique fingerprint.

Cite this