Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929554575065088 |
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| author | Ó, João Marcos do Lu, Guozhen Ponciano, Raoní |
| author_facet | Ó, João Marcos do Lu, Guozhen Ponciano, Raoní |
| contents | We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02262 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications Ó, João Marcos do Lu, Guozhen Ponciano, Raoní Analysis of PDEs We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions. |
| title | Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2302.02262 |