WIAS Preprint No. 1587, (2011)

$L^infty$-estimates for divergence operators on bad domains



Authors

  • ter Elst, A.F.M.
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35R05 47A60 35B65

Keywords

  • Elliptic equations, mixed Dirichlet-Neumann conditions, $L^infty$-estimates

Abstract

In this paper, we prove $L^infty$-estimates for solutions of divergence operators in case of mixed boundary conditions. In this very general setting, the Dirichlet boundary part may be arbitrarily wild, i.e. no regularity conditions have to be imposed on it.

Appeared in

  • Anal. Appl. (Singap.), 10 (2012) pp. 207--214.

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