Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications

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Hauptverfasser: Anthal, Gurdev Chand, Garain, Prashanta
Format: Preprint
Veröffentlicht: 2025
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author Anthal, Gurdev Chand
Garain, Prashanta
author_facet Anthal, Gurdev Chand
Garain, Prashanta
contents In this article, we establish Pohozaev-type identities for a class of quasilinear elliptic equations and systems involving both local and nonlocal $p$-Laplace operators. Specifically, we obtain these identities in $\mathbb{R}^n$ for the purely anisotropic $p$-Laplace equations, the purely fractional $p$-Laplace equations, as well as for equations that incorporate both anisotropic and fractional $p$-Laplace features. We also extend these results to the corresponding systems. To the best of our knowledge, the identities we derive in the mixed case are new even when $p=2$. Finally, we illustrate some of the applications of our main results.
format Preprint
id arxiv_https___arxiv_org_abs_2506_08667
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications
Anthal, Gurdev Chand
Garain, Prashanta
Analysis of PDEs
35R11, 35J92, 35A01, 35J62
In this article, we establish Pohozaev-type identities for a class of quasilinear elliptic equations and systems involving both local and nonlocal $p$-Laplace operators. Specifically, we obtain these identities in $\mathbb{R}^n$ for the purely anisotropic $p$-Laplace equations, the purely fractional $p$-Laplace equations, as well as for equations that incorporate both anisotropic and fractional $p$-Laplace features. We also extend these results to the corresponding systems. To the best of our knowledge, the identities we derive in the mixed case are new even when $p=2$. Finally, we illustrate some of the applications of our main results.
title Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications
topic Analysis of PDEs
35R11, 35J92, 35A01, 35J62
url https://arxiv.org/abs/2506.08667