涉及各向异性扩散系数的极奇椭圆方程弱解的连续可微性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-10-27 DOI:10.1515/acv-2022-0072

Shuntaro Tsubouchi

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引用次数: 3

摘要

摘要本文考虑了一类极奇异椭圆方程，该方程包含一个各向异性扩散算子，包括一个拉普拉斯算子，并被一个带1 ＆lt的p -拉普拉斯型扩散算子扰动;P ＆lt;∞{1＆lt;p＆lt;\infty}。这个方程在一个面附近，也就是梯度消失的地方，似乎很难解析处理。我们的主要目的是证明弱解即使在面上也是连续可微的。在这里，当一个梯度在一个面附近被截断时，它是否连续是有意义的。为了肯定地回答这个问题，我们考虑一个近似问题，并使用标准方法，包括德乔吉的截断和冻结系数方法。

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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Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity

Abstract In this paper we consider a very singular elliptic equation that involves an anisotropic diffusion operator, including the one-Laplacian, and is perturbed by a p -Laplacian-type diffusion operator with 1 < p < ∞ {1

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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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