DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION

doi:10.1007/s10473-026-0201-7

数学物理学报(英文版) ›› 2026, Vol. 46 ›› Issue (2): 519-528.doi: 10.1007/s10473-026-0201-7

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DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION

Shusen YAN¹, Huansong ZHOU^2,*

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. Center for Mathematical Sciences, Wuhan University of Technology, Wuhan 430070, China

收稿日期:2024-06-14 修回日期:2024-10-29 发布日期:2026-05-22

DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION

Shusen YAN¹, Huansong ZHOU^2,*

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. Center for Mathematical Sciences, Wuhan University of Technology, Wuhan 430070, China

Received:2024-06-14 Revised:2024-10-29 Published:2026-05-22
Contact: ^*Huansong ZHOU, E-mail: hszhou@whut.edu.cn
About author:Shusen YAN, E-mail: syan@ccnu.edu.cn
Supported by:
NSFC (11931012, 12471112, 12571118).

摘要/Abstract

摘要： Using the domain variation estimate, we give a new proof of the local Pohozaev identities for weak solutions of elliptic equations involving $p$-Laplacian operators under only $C^1$-regularity of the solutions. As an application, we obtain the Pohozaev identities for $C^1$ solution of $p$-Laplacian equation in $\mathbb{R}^N$ with $1<p<N$.

关键词: $p$-Laplacian equation, domain variation, Pohozaev identity

Abstract: Using the domain variation estimate, we give a new proof of the local Pohozaev identities for weak solutions of elliptic equations involving $p$-Laplacian operators under only $C^1$-regularity of the solutions. As an application, we obtain the Pohozaev identities for $C^1$ solution of $p$-Laplacian equation in $\mathbb{R}^N$ with $1<p<N$.

Key words: $p$-Laplacian equation, domain variation, Pohozaev identity

中图分类号:

35J92

Shusen YAN, Huansong ZHOU. DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION[J]. 数学物理学报(英文版), 2026, 46(2): 519-528.

Shusen YAN, Huansong ZHOU. DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION[J]. Acta mathematica scientia,Series B, 2026, 46(2): 519-528.

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DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION

DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION

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