有低阶项的非线性椭圆方程的诺依曼问题

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-26 DOI:10.1016/j.na.2024.113626

M.F. Betta , O. Guibé , A. Mercaldo

引用次数: 0

摘要

本文证明了原型为 λ|u|p-2u-Δpu-div(c(x)|u|p-2u)+b(x)|∇u|p-2∇u=finΩ 的非线性椭圆 Neumann 问题解的存在性结果、|∇u|p-2∇u+c(x)|u|p-2u⋅n̲=0∂Ω，其中 Ω 是 RN 的有界域，N≥2，具有 Lipschitz 边界，1<；p<N ，n̲是∂Ω的外单位法线，λ>0，基准 f 属于 W1,p(Ω) 的对偶空间或 Lebesgue 空间 L1(Ω)。最后，系数 b、c 属于适当的 Lebesgue 空间或洛伦兹空间。在系数 b 和 c 的小性假设下，证明了弱解或重规范化解的存在性结果。

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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Neumann problems for nonlinear elliptic equations with lower order terms

In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is $(\begin{matrix} λ {| u |}^{p - 2} u - Δ_{p} u - div (c (x) {| u |}^{p - 2} u) + b (x) {| \nabla u |}^{p - 2} \nabla u = f & in Ω, \\ ({| \nabla u |}^{p - 2} \nabla u + c (x) {| u |}^{p - 2} u) \cdot \underset{̲}{n} = 0 & on \partial Ω \end{matrix})$ where $Ω$ is a bounded domain of $R^{N}$ , $N \geq 2$ , with Lipschitz boundary, $1 < p < N$ , $\underset{̲}{n}$ is the outer unit normal to $\partial Ω$ , $λ > 0$ , the datum $f$ belongs to the dual space of $W^{1, p} (Ω)$ or to Lebesgue space $L^{1} (Ω)$ . Finally the coefficients $b$ , $c$ belong to appropriate Lebesgue spaces or Lorentz spaces.

Existence results for weak solutions or renormalized solutions are proved under smallness assumptions on the coefficients $b$ and $c$ .

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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.