On the boundary Harnack principle in Hölder domains

Daniela De Silva; Ovidiu Savin; Daniela De Silva; Ovidiu Savin

doi:10.3934/mine.2022004

Mathematics in Engineering

2022, Volume 4, Issue 1: 1-12. doi: 10.3934/mine.2022004

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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

Received: 07 May 2020 Accepted: 30 March 2021 Published: 13 April 2021

We investigate the boundary Harnack principle for uniformly elliptic operators in divergence form in Hölder domains of exponent $ \alpha > 0 $. We also deal with operators in nondivergence form with coefficient that remain constant in the graph direction.
- boundary Harnack principle,
- Hölder domains,
- divergence operators,
- non-divergence operators,
- Carleson estimate
Citation: Daniela De Silva, Ovidiu Savin. On the boundary Harnack principle in Hölder domains[J]. Mathematics in Engineering, 2022, 4(1): 1-12. doi: 10.3934/mine.2022004

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Abstract

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

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