Regularizing Effect for a Class of Maxwell-Schrödinger Systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929425524719616 |
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| author | Santana, Ayana Pinheiro de Castro de Miranda, Luís Henrique |
| author_facet | Santana, Ayana Pinheiro de Castro de Miranda, Luís Henrique |
| contents | In this paper we prove the existence and regularity of weak solutions for the following system \begin{align*} \begin{cases} -\mbox{div}(M(x)\nabla u) + g(x,u,v) = f \ \ \mbox{in} \ \ Ω\\ -\mbox{div}(M(x)\nabla v) = h(x,u,v) \ \ \mbox{in} \ \ Ω\\ \ \ \ \ \ u=v=0 \ \ \mbox{on} \ \ \partial Ω, \end{cases} \end{align*}
where $Ω$ is an open bounded subset of $\mathbb{R}^N$, for $N>2$, $f\in L^m(Ω)$, where $m>1$ and $h,\ g$ are two Carathéodory functions. We prove that under appropriate conditions on $g$ and $h$ there exist solutions which escape the predicted regularity by the classical Stampacchia's theory causing the so-called regularizing effect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10194 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularizing Effect for a Class of Maxwell-Schrödinger Systems Santana, Ayana Pinheiro de Castro de Miranda, Luís Henrique Analysis of PDEs 35B65, 35D99 In this paper we prove the existence and regularity of weak solutions for the following system \begin{align*} \begin{cases} -\mbox{div}(M(x)\nabla u) + g(x,u,v) = f \ \ \mbox{in} \ \ Ω\\ -\mbox{div}(M(x)\nabla v) = h(x,u,v) \ \ \mbox{in} \ \ Ω\\ \ \ \ \ \ u=v=0 \ \ \mbox{on} \ \ \partial Ω, \end{cases} \end{align*} where $Ω$ is an open bounded subset of $\mathbb{R}^N$, for $N>2$, $f\in L^m(Ω)$, where $m>1$ and $h,\ g$ are two Carathéodory functions. We prove that under appropriate conditions on $g$ and $h$ there exist solutions which escape the predicted regularity by the classical Stampacchia's theory causing the so-called regularizing effect. |
| title | Regularizing Effect for a Class of Maxwell-Schrödinger Systems |
| topic | Analysis of PDEs 35B65, 35D99 |
| url | https://arxiv.org/abs/2310.10194 |