Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form

Minoru Murata

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Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form

机译：偏积形式的抛物方程的唯一性定理和椭圆方程的马丁定理

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摘要

We give a method to determine Martin boundaries of product domains for elliptic equations in skew product form via Widder type uniqueness theorems for parabolic equations. It is shown that the fiber of the Martin boundary at infinity of the base space degenerates into one point if any nonnegative solution to the Dirichlet problem for a corresponding parabolic equation with zero initial and boundary data is identically zero. We apply it in a unified way to several concrete examples to explicitly determine Martin boundaries for them.

机译：我们给出了一种通过抛物方程的Widder型唯一性定理来确定偏积形式的椭圆方程的乘积域的马丁边界的方法。结果表明，如果初始和边界数据为零的相应抛物方程的Dirichlet问题的任何非负解都为零，则基空间无穷大处的马丁边界的纤维退化为一个点。我们以统一的方式将其应用于几个具体示例，以明确为其确定马丁边界。

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来源
《Journal of the Mathematical Society of Japan》 |2005年第2期|p.387-413|共27页
作者
Minoru Murata;
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作者单位

Department of Mathematics Tokyo Institute of Technology Oh-okayama, Meguro-ku, Tokyo, 152-8551 Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
uniqueness of nonnegative solutions; parabolic equation; positive solution; elliptic equation; skew product; Martin boundary;

机译：非负解的唯一性;抛物方程;正解;椭圆方程;偏积;马丁边界;

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1. A Parabolic Approach to Martin Boundaries for Elliptic Equations in Skew Product Form [J] . Minoru Murata, Noriaki Suzuki Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2014,第3期

机译：椭圆积形式椭圆方程的马丁边界抛物线法
2. Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations [J] . Murata M. Journal of Functional Analysis . 2002,第1期

机译：椭圆偏积的马丁边界，半小扰动和抛物线方程的基本解
3. Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries [J] . Murata M Journal of Functional Analysis . 2007,第1期

机译：抛物线方程和椭圆马丁边界的非负解的积分表示
4. Boundary Unique Continuation for Stochastic Parabolic Equations [C] . LI Hongheng, Lü Qi 2012 31st Chinese Control Conference. . -1

机译：随机抛物方程的边界唯一连续
5. Unique Continuation for Parabolic and Elliptic Equations and Analyticity Results for Euler and Navier Stokes Equations [D] . Camliyurt, Guher. 2018

机译：抛物线和椭圆方程的独特延续和欧拉和Navier Stokes方程的分析结果
6. Linear Parabolic Differential Equations of Arbitrary Order; General Boundary-Value Problems for Elliptic Equations [O] . Felix E. Browder 1953

机译：任意阶线性抛物线方程椭圆方程的一般边值问题
7. Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form [O] . Minoru MURATA 2005

机译：抛物方程的唯一性定理和椭圆形式的椭圆方程中的椭圆形界限

Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form

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