The boundary Harnack principle in H\"{o}lder domains with a strong regularity
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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.
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.
참고문헌 (7)
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