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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.
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참고문헌 (7)
참고문헌 신청
A. D. Aleksandrov / 1963 / Uniqueness conditions and estimates for the solution of the Dirichlet problem / English transl.:Amer. Math. Soc. Transl. (2) 68:89~119
R. F. Bass / 1994 / The boundary Harnack principle for non-divergence form elliptic operators / J. London Math. Soc 50:157~169
H. Kim / 2011 / Carleson type estimates for second order elliptic equations with unbounded drift / J. Math. Sci 176(6):928~944
H. Kim / 2011 / Boundary Harnack principle for second order elliptic equations with unbounded drift / J. Math. Sci 179(1):127~143
H. Kim / 2014 / The boundary Harnack principle for second order elliptic equations in John and Uniform domains / Proceedings of the St. Petersburg Mathematical Society 15:153~176
R. F. Bass / 1994 / The boundary Harnack principle for non-divergence form elliptic operators / J. London Math. Soc 50:157~169
H. Kim / 2011 / Carleson type estimates for second order elliptic equations with unbounded drift / J. Math. Sci 176(6):928~944
H. Kim / 2011 / Boundary Harnack principle for second order elliptic equations with unbounded drift / J. Math. Sci 179(1):127~143
H. Kim / 2014 / The boundary Harnack principle for second order elliptic equations in John and Uniform domains / Proceedings of the St. Petersburg Mathematical Society 15:153~176
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