| Abstract: |
| 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 H\"{o}lder continuity of the solution.
Moreover, Gaussian H\"{o}lder estimates for the corresponding heat
kernel are derived.
This is joint work with Joachim Rehberg. |
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