An elliptic problem in dimension N with a varying drift term bounded in LN

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-29 DOI:10.3233/asy-241914

Juan Casado-Díaz

引用次数: 0

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 LN(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 H01(Ω). However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in (J. Differential Equations 258 (2015) 2290–2314), and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems.

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维数为 N 的椭圆问题，其漂移项的变化在 LN 中有界

本文致力于研究一连串带有变化漂移项的线性椭圆方程的渐近行为，这些方程的系数在 LN(Ω)中是有界的，N 是空间的维数。众所周知，在索波列夫空间 H01(Ω)中，这些问题都存在唯一的解。然而，由于算子不是强制的，因此在这个空间中的解没有统一的估计值。我们利用《微分方程学报》（J. Differential Equations 258 (2015) 2290-2314）中的一些估计，以及通过添加一个小的非线性一阶项获得的正则化，来达到这些问题的极限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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