Continuous bounds for quotients of Green functions
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.
scientific article; zbMATH DE number 4025811