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摘要
In this paper, we investigate linear elliptic, second-order boundary value problems with mixed boundary conditions on domains with a rough boundary. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain including a very weak compatibility condition between the Dirichlet boundary part and its complement we prove first Holder continuity of the solution. Secondly, Gaussian Holder estimates for the corresponding heat kernel are derived.
- 出版日期2015-4
