Regularizing effect of absorption terms in singular and degenerate elliptic problems
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866914991081259008 |
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| author | Sbai, Abdelaaziz Hadfi, Youssef El |
| author_facet | Sbai, Abdelaaziz Hadfi, Youssef El |
| contents | In this paper we study the existence and regularity of solutions to the following singular problem \begin{equation} \left\{ \begin{array}{lll} &-\displaystyle\mbox{div} \big(a(x,u)|\nabla u|^{p-2}|\nabla u|\big) + |u|^{s-1}u =\frac{f}{u^γ} &\mbox{ in } Ω\\ &u>0 &\mbox{ in }Ω\\ &u=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2008_03597 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Regularizing effect of absorption terms in singular and degenerate elliptic problems Sbai, Abdelaaziz Hadfi, Youssef El Analysis of PDEs 35A21, 35B20, 35B25, 35B45, 35D30, 35J60, 35J70, 35J75 In this paper we study the existence and regularity of solutions to the following singular problem \begin{equation} \left\{ \begin{array}{lll} &-\displaystyle\mbox{div} \big(a(x,u)|\nabla u|^{p-2}|\nabla u|\big) + |u|^{s-1}u =\frac{f}{u^γ} &\mbox{ in } Ω\\ &u>0 &\mbox{ in }Ω\\ &u=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} proving that the lower order term $u|u|^{s-1}$ has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity. |
| title | Regularizing effect of absorption terms in singular and degenerate elliptic problems |
| topic | Analysis of PDEs 35A21, 35B20, 35B25, 35B45, 35D30, 35J60, 35J70, 35J75 |
| url | https://arxiv.org/abs/2008.03597 |