Marcinkiewicz Estimates for Solutions of Some Elliptic Problems with Singular Data

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-05-03 DOI:10.1007/s11118-024-10140-w

Lucio Boccardo, Luigi Orsina

引用次数: 0

Abstract

In this paper we prove regularity result for solutions of the boundary value problem

$$ \left\{ \begin{array}{cl} -{{\,\textrm{div}\,}}(M(x)\,\nabla u) + u = -{{\,\textrm{div}\,}}(u\,E(x)) + f(x)\,, &{} \text{ in }\,\, \Omega , \\ u = 0\,, &{} \text{ on }\,\,\partial \Omega , \end{array} \right. $$

with the vector field E(x) and the function f(x) belonging to some Marcinkiewicz spaces.

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具有奇异数据的某些椭圆问题解的 Marcinkiewicz 估计数

本文证明了边界值问题解的正则性结果 $$ \left\{ \begin{array}{cl} -{\textrm{div}\,}}(M(x)\,\nabla u) + u = -{\textrm{div}\,}}(u\,E(x))+ f(x)\,, &{}\u = 0\,, &{}\text{ on }\,\partial\Omega , \end{array}\是的$$with the vector field E(x) and the function f(x) belonging to some Marcinkiewicz spaces.

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.