Sharp higher order Admas' inequality with exact growth condition on weighted Sobolev spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910661745836032 |
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| author | Ó, João Marcos do Lu, Guozhen Ponciano, Raoní |
| author_facet | Ó, João Marcos do Lu, Guozhen Ponciano, Raoní |
| contents | This paper introduces a novel higher order Adams inequality that incorporates an exact growth condition for a class of weighted Sobolev spaces. Our rigorous proof confirms the validity of this inequality and provides insights into the optimal nature of the critical constant and the exponent within the denominator. Furthermore, we apply this inequality to study a class of ordinary differential equations (ODEs), where we successfully derive both a concept of the weak solution and a comprehensive regularity theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08566 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp higher order Admas' inequality with exact growth condition on weighted Sobolev spaces Ó, João Marcos do Lu, Guozhen Ponciano, Raoní Analysis of PDEs Classical Analysis and ODEs 35J35, 35B33, 46E30 This paper introduces a novel higher order Adams inequality that incorporates an exact growth condition for a class of weighted Sobolev spaces. Our rigorous proof confirms the validity of this inequality and provides insights into the optimal nature of the critical constant and the exponent within the denominator. Furthermore, we apply this inequality to study a class of ordinary differential equations (ODEs), where we successfully derive both a concept of the weak solution and a comprehensive regularity theory. |
| title | Sharp higher order Admas' inequality with exact growth condition on weighted Sobolev spaces |
| topic | Analysis of PDEs Classical Analysis and ODEs 35J35, 35B33, 46E30 |
| url | https://arxiv.org/abs/2309.08566 |