(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Hieber, Matthias; Rehberg, Joachim
In this paper we investigate quasilinear systems of reaction-diffusion
equations with mixed Dirichlet-Neumann bondary conditions on non smooth
domains. Using techniques from maximal regularity and heat-kernel estimates
we prove existence of a unique solution to systems of this type.
(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Elschner, Johannes; Rehberg, Joachim; Schmidt, Gunther
We prove an optimal regularity result for elliptic operators $-nabla cdot mu nabla:W^1,q_0 rightarrow W^-1,q$ for a $q>3$ in the case when the coefficient function $mu$ has a jump across a $C^1$ interface and is continuous elsewhere. A counterexample shows that the $C^1$ condition cannot be relaxed in general. Finally, we draw some conclusions for corresponding parabolic operators.
