Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908338893094912 |
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| author | Akagi, Goro Miyakawa, Hiroki |
| author_facet | Akagi, Goro Miyakawa, Hiroki |
| contents | This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of $p$-Laplacian type with absorption and (prescribed) locally integrable forcing posed in (possibly unbounded) Lipschitz domains. In particular, the forcing terms may not belong to the dual space of an energy space, e.g., $W^{1,p}_{\rm loc}$, which is necessary for the existence of weak (or energy) solutions of class $W^{1,p}_{\rm loc}$. The method of a proof relies on both local energy estimates and a relative truncation technique developed by Bulíček and Schwarzacher (Calc. Var. PDEs in 2016), where the bounded domain case is studied for (globally) integrable forcing. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing Akagi, Goro Miyakawa, Hiroki Analysis of PDEs 35J92, 35J57 This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of $p$-Laplacian type with absorption and (prescribed) locally integrable forcing posed in (possibly unbounded) Lipschitz domains. In particular, the forcing terms may not belong to the dual space of an energy space, e.g., $W^{1,p}_{\rm loc}$, which is necessary for the existence of weak (or energy) solutions of class $W^{1,p}_{\rm loc}$. The method of a proof relies on both local energy estimates and a relative truncation technique developed by Bulíček and Schwarzacher (Calc. Var. PDEs in 2016), where the bounded domain case is studied for (globally) integrable forcing. |
| title | Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing |
| topic | Analysis of PDEs 35J92, 35J57 |
| url | https://arxiv.org/abs/2410.00585 |