Characterizations of the viscosity solution of a nonlocal and nonlinear equation induced by the fractional p-Laplace and the fractional p-convexity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-01-27 DOI:10.1515/acv-2021-0110

S. Shi, Zhichun Zhai, Lei Zhang

引用次数: 1

Abstract

Abstract In this paper, when studying the connection between the fractional convexity and the fractional p-Laplace operator, we deduce a nonlocal and nonlinear equation. Firstly, we will prove the existence and uniqueness of the viscosity solution of this equation. Then we will show that u ⁢ ( x ) {u(x)} is the viscosity sub-solution of the equation if and only if u ⁢ ( x ) {u(x)} is so-called ( α , p ) {(\alpha,p)} -convex. Finally, we will characterize the viscosity solution of this equation as the envelope of an ( α , p ) {(\alpha,p)} -convex sub-solution. The technique involves attainability of the exterior datum and a comparison principle for the nonlocal and nonlinear equation.

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分数阶p-拉普拉斯和分数阶p-凸性引起的非局部非线性方程的粘性解的表征

摘要本文在研究分数阶凸性与分数阶p-拉普拉斯算子的关系时，导出了一个非局部非线性方程。首先，我们将证明该方程黏度解的存在唯一性。然后我们将证明，当且仅当u≠(x) {u(x)}是所谓的(α，p) {(\ α，p)} -凸时，u≠(x) {u(x)}是方程的粘度子解。最后，我们将把这个方程的粘度解描述为(α，p) {(\ α，p)} -凸子解的包络线。该技术涉及到外部基准的可得性以及非局部和非线性方程的比较原理。

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

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.

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