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

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H. Hueber; M. Sieveking
Uniform bounds for quotients of Green functions on $C^{1,1}$-domains
Annales de l'institut Fourier, 32 no. 1 (1982), p. 105-117, doi: 10.5802/aif.861
Article PDF | Reviews MR 84a:35063 | Zbl 0465.35028

Résumé - 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 $c>0$ depending only on the Hölder norms of the coefficients of $L$ and its constant of ellipticity such that

$$ c^{-1}G^\Omega _\Delta \le G^\Omega _L \le c G^\Omega _\Delta \text{on} \Omega \times \Omega ,$$

where $\gamma ^\Omega _\Delta $ (resp. $G^\Omega _L$) are the Green functions of $\Delta $ (resp. $L$) on $\Omega $.

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