Boundary Harnack Principle on Uniform Domains

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-07-22 DOI:10.1007/s11118-024-10154-4

Aobo Chen

引用次数: 0

Abstract

We present a proof of scale-invariant boundary Harnack principle for uniform domains when the underlying space satisfies a scale-invariant elliptic Harnack inequality. Our approach does not assume the underlying space to be geodesic. Additionally, the existence of Green functions is also not assumed beforehand and is ensured by a recent result from M. T. Barlow, Z.-Q. Chen and M. Murugan.

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均匀域上的边界哈纳克原理

我们提出了当底层空间满足尺度不变的椭圆哈纳克不等式时，均匀域的尺度不变边界哈纳克原理的证明。我们的方法不假定底层空间是测地线。此外，我们也不事先假定格林函数的存在，而是通过 M. T. Barlow、Z.-Q. Chen 和 M. Murugan 的最新成果来确保格林函数的存在。Chen 和 M. Murugan 的最新成果确保了格林函数的存在。

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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.