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Continuous bounds for quotients of Green functions. (English) Zbl 0631.31004
For uniformly elliptic partial differential operators of second order defined on a bounded domain of \({\mathbb{R}}^ n\), with coefficients belonging to a Hölder-class, the paper introduces the coefficients- topology (uniform on compacta-convergence of coefficients). This enables the authors to get uniform bounds of the corresponding quotients of Green kernels. In other words, a distance through the Green functions of the corresponding operators gives the preceding topology on the coefficients. Methods uses classical potential theory.
Reviewer: O.Gebuhrer

MSC:
31B35 Connections of harmonic functions with differential equations in higher dimensions
35J25 Boundary value problems for second-order elliptic equations
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