Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications
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arXiv
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| Format: | Preprint |
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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 |