Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(6): 1741-1751

Online first article September 21, 2016      Printed November 30, 2016

https://doi.org/10.4134/BKMS.b150914

Copyright © The Korean Mathematical Society.

The boundary Harnack principle in H\"{o}lder domains with a strong regularity

Hyejin Kim

University of Michigan--Dearborn

Abstract

We prove the boundary Harnack principle and the Carleson type estimate for ratios of solutions $u/v$ of non--divergence second order elliptic equations $Lu=a_{ij}D_{ij}u+b_{i}D_{i}u=0$ in a bounded domain $\Omega\subset\mathbb{R}^{n}$. We assume that $b_{i}\in L^n(\Omega)$ and $\Omega$ is a H\"{o}lder domain of order $\alpha\in (0,1)$ satisfying a strong regularity condition.

Keywords: boundary Harnack principle, Carleson type estimates, elliptic equations with measurable coefficients

MSC numbers: Primary 35B05; Secondary 35J15

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