An elliptic problem in dimension N with a varying drift term bounded in $L^N$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914703424356352 |
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| author | Casado-Díaz, Juan |
| author_facet | Casado-Díaz, Juan |
| contents | The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in $L^N(Ω)$, with $N$ the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space $H^1_0(Ω)$. However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in \cite{boc1}, and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elliptic problem in dimension N with a varying drift term bounded in $L^N$ Casado-Díaz, Juan Analysis of PDEs 35B27 The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in $L^N(Ω)$, with $N$ the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space $H^1_0(Ω)$. However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in \cite{boc1}, and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems. |
| title | An elliptic problem in dimension N with a varying drift term bounded in $L^N$ |
| topic | Analysis of PDEs 35B27 |
| url | https://arxiv.org/abs/2403.03115 |