Potential estimates for fully nonlinear elliptic equations with bounded ingredients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-09-05 DOI:10.3934/mine.2023063

Edgard A. Pimentel, Miguel Walker

引用次数: 1

Abstract

We examine $ L^p $-viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering $ p_0 < p < d $, we focus on gradient-regularity estimates stemming from nonlinear potentials. We find conditions for local Lipschitz-continuity of the solutions and continuity of the gradient. We survey recent breakthroughs in regularity theory arising from (nonlinear) potential estimates. Our findings follow from – and are inspired by – fundamental facts in the theory of $ L^p $-viscosity solutions, and results in the work of Panagiota Daskalopoulos, Tuomo Kuusi and Giuseppe Mingione ^[10].

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具有有界成分的完全非线性椭圆方程的势估计

我们研究了具有有界可测成分的完全非线性椭圆方程的L^p -粘度解。通过考虑$ p_0 < p < d $，我们关注于非线性势的梯度正则性估计。我们找到了解的局部lipschitz -连续性和梯度的连续性的条件。我们调查了由(非线性)势估计引起的正则性理论的最新突破。我们的发现遵循并受到L^p -粘度解理论中的基本事实的启发，并在Panagiota Daskalopoulos, Tuomo Kuusi和Giuseppe Mingione bbb的工作中得到结果。

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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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.