Wiener-type tests from a two-sided Gaussian bound
Wiener-type tests from a two-sided Gaussian bound
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两侧高斯界的维纳型检验
DOI：
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发表时间：
2015
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通讯作者：
Francesco Uguzzoni
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作者：
E. Lanconelli;G. Tralli;Francesco Uguzzoni
本文研究了亚椭圆扩散算子H.我们的主要目的是显示，与公理化的方法，一个维纳型测试的$$mathcal {H}$$H-正则性的边界点，可以从以下基本假设：高斯边界的基本解决方案$$mathcal {H}$$H关于一个距离满足加倍条件和部分性质。作为实现这一结果的主要步骤，我们建立了一些估计的边界上的连续性模的广义Perron-Wiener解决方案的相关Dirichlet问题。估计涉及维纳型系列，与高斯边界上建模的能力。最后在适当的外锥条件下证明了解的边界Hölder估计。
In this paper, we are concerned with hypoelliptic diffusion operators $$mathcal {H}$$H. Our main aim is to show, with an axiomatic approach, that a Wiener-type test of $$mathcal {H}$$H-regularity of boundary points can be derived starting from the following basic assumptions: Gaussian bounds of the fundamental solution of $$mathcal {H}$$H with respect to a distance satisfying doubling condition and segment property. As a main step toward this result, we establish some estimates at the boundary of the continuity modulus for the generalized Perron–Wiener solution to the relevant Dirichlet problem. The estimates involve Wiener-type series, with the capacities modeled on the Gaussian bounds. We finally prove boundary Hölder estimates of the solution under a suitable exterior cone condition.