Nonlinear variable exponent Picone identity and $p(x)$-sub-Laplacian first eigenvalue for general vector fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917685274607616 |
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| author | Abolarinwa, Abimbola |
| author_facet | Abolarinwa, Abimbola |
| contents | In this paper, we establish a new generalized nonlinear variable exponent Picone identities for $p(x)$-sub-Laplacian. As applications we prove uniqueness, simplicity, momotonicity and isolatedness of the first nontrivial Dirichlet eigenvalue of $p(x)$-sub-Laplacian with respect to the general vector fields. Further applications yield Hardy type inequalities and Caccioppolli estimates with variable exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05642 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonlinear variable exponent Picone identity and $p(x)$-sub-Laplacian first eigenvalue for general vector fields Abolarinwa, Abimbola Analysis of PDEs 35B05 35H20, 35P30, 47J10 In this paper, we establish a new generalized nonlinear variable exponent Picone identities for $p(x)$-sub-Laplacian. As applications we prove uniqueness, simplicity, momotonicity and isolatedness of the first nontrivial Dirichlet eigenvalue of $p(x)$-sub-Laplacian with respect to the general vector fields. Further applications yield Hardy type inequalities and Caccioppolli estimates with variable exponents. |
| title | Nonlinear variable exponent Picone identity and $p(x)$-sub-Laplacian first eigenvalue for general vector fields |
| topic | Analysis of PDEs 35B05 35H20, 35P30, 47J10 |
| url | https://arxiv.org/abs/2209.05642 |