WIAS Preprint No. 1977, (2014)

Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems



Authors

  • Disser, Karoline
  • Kaiser, Hans-Christoph
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35J25 35R05 35B65

Keywords

  • Second-order divergence operators, elliptic regularity, mixed boundary conditions, discontinuous coefficients

Abstract

On bounded three-dimensional domains, we consider divergence-type operators including mixed homogeneous Dirichlet and Neumann boundary conditions and discontinuous coefficient functions. We develop a geometric framework in which it is possible to prove that the operator provides an isomorphism of suitable function spaces. In particular, in these spaces, the gradient of solutions turns out to be integrable with exponent larger than the space dimension three. Relevant examples from real-world applications are provided in great detail.

Appeared in

  • SIAM J. Math. Anal., 47 (2015) pp. 1719--1746.

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