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

Prashanta Garain, Wontae Kim, Juha Kinnunen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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
Pages (from-to)697-715
Number of pages19
JournalForum Mathematicum
Volume36
Issue number3
DOIs
StatePublished - 1 May 2024
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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