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Research Article | Open Access

Harnack inequality for a p-Laplacian equation with a source reaction term involving the product of the function and its gradient

Bo Chen, Junhui Xie( )
School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, China
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Abstract

A p-Laplacian type problem with a source reaction term involving the product of the function and its gradient is considered in this paper. A Harnack inequality is proved, and the main idea is based on de Giorgi-Nash-Moser iteration and Moser's iteration technique. As a consequence, H o ¨ l d e r continuity and boundness for the solution of this problem also are obtained.

Keywords

p-LaplaceHarnack inequalityde Giorgi-Nash-Moser iterationMoser's iteration

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Electronic Research Archive
Volume 31 Issue 2,
February 2023
Pages 1157-1169
DOI: 10.3934/era.2023059

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Cite this article:
Chen B, Xie J. Harnack inequality for a p-Laplacian equation with a source reaction term involving the product of the function and its gradient. Electronic Research Archive, 2023, 31(2): 1157-1169. https://doi.org/10.3934/era.2023059

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Received: 26 September 2022
Revised: 03 December 2022
Accepted: 11 December 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)