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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.10607 |
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| _version_ | 1866929421216120832 |
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| author | Della Pietra, Francesco di Blasio, Giuseppina Radice, Teresa |
| author_facet | Della Pietra, Francesco di Blasio, Giuseppina Radice, Teresa |
| contents | In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{cases} -\text{div}(b(|u|)\nabla u)=f &\text{in }Ω,\\[.2cm] \displaystyle\frac{\partial u}{\partial ν}+βu=0 &\text{on }\partialΩ\end{cases} $$ where $Ω$ is a bounded Lipschitz domain in $\mathbb R^N$, $N>2$, $β>0$, $b(s)$ is a positive function which may vanish at infinity and $f$ belongs to a suitable Lebesgue space. The presence of such a function $b$ in the principal part of the operator prevents it from being uniformly elliptic when $u$ is large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and regularity results for a class of non-uniformly elliptic Robin problems Della Pietra, Francesco di Blasio, Giuseppina Radice, Teresa Analysis of PDEs In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: $$ \begin{cases} -\text{div}(b(|u|)\nabla u)=f &\text{in }Ω,\\[.2cm] \displaystyle\frac{\partial u}{\partial ν}+βu=0 &\text{on }\partialΩ\end{cases} $$ where $Ω$ is a bounded Lipschitz domain in $\mathbb R^N$, $N>2$, $β>0$, $b(s)$ is a positive function which may vanish at infinity and $f$ belongs to a suitable Lebesgue space. The presence of such a function $b$ in the principal part of the operator prevents it from being uniformly elliptic when $u$ is large. |
| title | Existence and regularity results for a class of non-uniformly elliptic Robin problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.10607 |