On the regularity theory for mixed anisotropic and nonlocal<i>p</i>-Laplace equations and its applications to singular problems-Reference-Cited by-同舟云学术

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

Published:2023-10-27 Issue:0 Volume:0 Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Garain Prashanta¹,Kim Wontae²,Kinnunen Juha²

Affiliation:

1. Department of Mathematical Sciences , Indian Institute of Science Education and Research Berhampur , Berhampur , Odisha 760010 , India

2. Department of Mathematics , Aalto University , P.O. BOX 11100, 00076 , Espoo , Finland

Abstract

AbstractWe establish existence results for a class of mixed anisotropic and nonlocalp-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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0151/pdf

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