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- ItemOptimal regularity for elliptic transmission problems including C1 interfaces(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Elschner, Johannes; Rehberg, Joachim; Schmidt, GuntherWe 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.
- ItemEssential boundedness for solutions of the Neumann problem on general domains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) ter Elst, A.F.M.; Meinlschmidt, Hannes; Rehberg, JoachimLet the domain under consideration be bounded. Under the suppositions of very weak Sobolev embeddings we prove that the solutions of the Neumann problem for an elliptic, second order divergence operator are essentially bounded, if the right hand sides are taken from the dual of a Sobolev space which is adapted to the above embedding.