Existence of a Renormalized Solution of a Quasilinear Elliptic Equation without the Sign Condition on the Lower-Order Term

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-09-19 DOI:10.1134/s0012266124060041

L. M. Kozhevnikova

引用次数: 0

Abstract

The paper considers a second-order quasilinear elliptic equation with an integrable right-hand side. Restrictions on the structure of the equation are stated in terms of the generalized \(N \)-function. Unlike the author’s previous papers, there is no sign condition on the lower-order term of the equation. The existence of a renormalized solution of the Dirichlet problem for this equation is proved in nonreflexive Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.

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准线性椭圆方程不带下阶项符号条件的重规范化解的存在性

摘要本文研究了一个二阶准线性椭圆方程，其右手边为整数。用广义 \(N \)函数说明了对方程结构的限制。与作者以前的论文不同，方程的低阶项没有符号条件。在任意无界严格 Lipschitz 域中的非反射 Musielak-Orlicz-Sobolev 空间中证明了该方程的 Dirichlet 问题重规范化解的存在性。

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

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.