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 $1<p<N$.
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
.
DOI: 10.1007/s10473-026-0201-7
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