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

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis 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

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.