Global Weighted Lorentz Estimates of Oblique Tangential Derivative Problems for Weakly Convex Fully Nonlinear Operators

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-23 DOI:10.1007/s11118-024-10156-2

Junior da S. Bessa, Gleydson C. Ricarte

引用次数: 0

Abstract

In this work, we develop weighted Lorentz-Sobolev estimates for viscosity solutions of fully nonlinear elliptic equations with oblique boundary condition under weakened convexity conditions in the following configuration:

$$\left\{ \begin{array}{rclcl} F(D^2u,Du,u,x) & =& f(x)& \text {in} & \Omega \\ \beta \cdot Du + \gamma u& =& g & \text {on}& \partial \Omega ,\end{array}\right. $$

where $\Omega $ is a bounded domain in $\mathbb {R}^{n}$ ($n\ge 2$), under suitable assumptions on the source term f, data $\beta , \gamma $ and g. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.

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弱凸全非线性算子斜切向衍生问题的全局加权洛伦兹估计值

在这项工作中，我们针对具有斜边界条件的全非线性椭圆方程的粘性解，在弱化凸性条件下开发了加权洛伦兹-索博列夫估计，其配置如下： $$\left\{ \begin{array}{rclcl}F(D^2u,Du,u,x) & =& f(x)& \text {in} & \Omega \\beta \cdot Du + \gamma u& =& g & \text {on}& \partial \Omega ,\end{array}\right.此外，我们还得到了障碍问题解的洛伦兹-索博列夫估计和其他应用。

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.