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arXiv · 2403.03115

An elliptic problem in dimension N with a varying drift term bounded in $L^N$

Juan Casado-Díaz
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Abstract

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.

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Juan Casado-Díaz. 2024-03-05. An elliptic problem in dimension N with a varying drift term bounded in $L^N$. https://arxiv.org/abs/2403.03115

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