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; Bo Chen; Junhui Xie

doi:10.3934/era.2023059

Electronic Research Archive

2023, Volume 31, Issue 2: 1157-1169. doi: 10.3934/era.2023059

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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

Received: 26 September 2022 Revised: 03 December 2022 Accepted: 11 December 2022 Published: 27 December 2022

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\ddot{o}lder $ continuity and boundness for the solution of this problem also are obtained.
- p-Laplace,
- Harnack inequality,
- de Giorgi-Nash-Moser iteration,
- Moser's iteration
Citation: Bo Chen, Junhui Xie. Harnack inequality for a p-Laplacian equation with a source reaction term involving the product of the function and its gradient[J]. Electronic Research Archive, 2023, 31(2): 1157-1169. doi: 10.3934/era.2023059

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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\ddot{o}lder $ continuity and boundness for the solution of this problem also are obtained.

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