WIAS Preprint No. 2574, (2019)

Essential boundedness for solutions of the Neumann problem on general domains


Authors

  • ter Elst, A. F. M.
  • Meinlschmidt, Hannes
    ORCID: 0000-0002-5874-8017
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35D10 46E35

Keywords

  • Regularity, Neumann problem, elliptic operators

DOI

10.20347/WIAS.PREPRINT.2574

Abstract

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.

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