Uniform bounds for quotients of Green functions on $C^{1,1}$-domains

Hueber, H., and Sieveking, M.. "Uniform bounds for quotients of Green functions on $C^{1,1}$-domains." Annales de l'institut Fourier 32.1 (1982): 105-117. <http://eudml.org/doc/74520>.

@article{Hueber1982,
abstract = {Let $\Delta u = \Sigma _i \{\partial ^2 \over \partial ^2_\{x_i\}\}$, $Lu = \Sigma _\{i,j\} a_\{ij\} \{\partial ^2 \over \partial x_i \partial x_j\} u + \Sigma _i b_i \{\partial \over \partial x_i\} u + cu$ be elliptic operators with Hölder continuous coefficients on a bounded domain $\Omega \subset \{\bf R\}^n$ of class $C^\{1,1\}$. There is a constant $c&gt;0$ depending only on the Hölder norms of the coefficients of $L$ and its constant of ellipticity such that\begin\{\} c^\{-1\}G^\Omega \_\Delta \le G^\Omega \_L \le c G^\Omega \_\Delta \text\{on\} \Omega \times \Omega ,\end\{\}where $\gamma ^\Omega _\Delta $ (resp. $G^\Omega _L$) are the Green functions of $\Delta $ (resp. $L$) on $\Omega $.},
author = {Hueber, H., Sieveking, M.},
journal = {Annales de l'institut Fourier},
keywords = {Green's functions; Hölder continuous coefficients},
language = {eng},
number = {1},
pages = {105-117},
publisher = {Association des Annales de l'Institut Fourier},
title = {Uniform bounds for quotients of Green functions on $C^\{1,1\}$-domains},
url = {http://eudml.org/doc/74520},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Hueber, H.
AU - Sieveking, M.
TI - Uniform bounds for quotients of Green functions on $C^{1,1}$-domains
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 1
SP - 105
EP - 117
AB - Let $\Delta u = \Sigma _i {\partial ^2 \over \partial ^2_{x_i}}$, $Lu = \Sigma _{i,j} a_{ij} {\partial ^2 \over \partial x_i \partial x_j} u + \Sigma _i b_i {\partial \over \partial x_i} u + cu$ be elliptic operators with Hölder continuous coefficients on a bounded domain $\Omega \subset {\bf R}^n$ of class $C^{1,1}$. There is a constant $c&gt;0$ depending only on the Hölder norms of the coefficients of $L$ and its constant of ellipticity such that\begin{} c^{-1}G^\Omega _\Delta \le G^\Omega _L \le c G^\Omega _\Delta \text{on} \Omega \times \Omega ,\end{}where $\gamma ^\Omega _\Delta $ (resp. $G^\Omega _L$) are the Green functions of $\Delta $ (resp. $L$) on $\Omega $.
LA - eng
KW - Green's functions; Hölder continuous coefficients
UR - http://eudml.org/doc/74520
ER -