Lipschitz 域中系数无界的亚线性椭圆方程

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-07-30 DOI:10.1007/s00025-024-02246-9

Kentaro Hirata

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引用次数: 0

摘要

本文关注的是在 Lipschitz 域中系数无界的亚线性椭圆方程的同质 Dirichlet 问题。作为边界哈纳克原理的副产品，本文提出了正解的双边先验估计及其梯度的先验上限估计。通过这些估计值，我们可以证明，与光滑域不同，在没有法导数信息的情况下，均质德里赫特问题正解的唯一性。

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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Sublinear Elliptic Equations with Unbounded Coefficients in Lipschitz Domains

This paper is concerned with the homogeneous Dirichlet problem for a sublinear elliptic equation with unbounded coefficients in a Lipschitz domain. Bilateral a priori estimates for positive solutions and a priori upper estimates for their gradients are presented as a byproduct of the boundary Harnack principle. These estimates allow us to show the uniqueness of a positive solution of the homogeneous Dirichlet problem under no information about normal derivatives unlike in smooth domains.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.