Essential boundedness for solutions of the Neumann problem on general domains
- ter Elst, A. F. M.
- Meinlschmidt, Hannes
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 35D10 46E35
- Regularity, Neumann problem, elliptic operators
Let 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.