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Research Article | Open Access

On the boundary Harnack principle in Hölder domains

Daniela De Silva( ), Ovidiu Savin
Department of Mathematics, Barnard College, Columbia University, New York, NY 10027, USA
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Abstract

We investigate the boundary Harnack principle for uniformly elliptic operators in divergence form in Hölder domains of exponent α > 0. We also deal with operators in nondivergence form with coefficient that remain constant in the graph direction.

Keywords

boundary Harnack principleHölder domainsdivergence operatorsnon-divergence operatorsCarleson estimate

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Mathematics in Engineering
Volume 4 Issue 1,
February 2022
Pages 1-12
DOI: 10.3934/mine.2022004

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Cite this article:
De Silva D, Savin O. On the boundary Harnack principle in Hölder domains. Mathematics in Engineering, 2022, 4(1): 1-12. https://doi.org/10.3934/mine.2022004

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Received: 07 May 2020
Accepted: 30 March 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)