维数为 N 的椭圆问题，其漂移项的变化在 LN 中有界

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Asymptotic Analysis Pub Date : 2024-05-29 DOI:10.3233/asy-241914

Juan Casado-Díaz

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引用次数: 0

摘要

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

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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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.