WIAS Preprint No. 2705, (2020)

Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations


Authors

  • Meinlschmidt, Hannes
    ORCID: 0000-0002-5874-8017
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35J25 35B65 35R05 35Q81 92E20

Keywords

  • Elliptic regularity, nonsmooth geometry, Sneiberg stability theorem, fractional Sobolev spaces, van Roosbroeck system, semiconductor equations

DOI

10.20347/WIAS.PREPRINT.2705

Abstract

In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order Xs-1,qD(Ω) for s > 0 small, including mixed boundary conditions and with a fully nonsmooth geometry of Ω and the Dirichlet boundary part D. We expect the result to find applications in the analysis of nonlinear parabolic equations, in particular for quasilinear problems or when treating coupled systems of equations. To demonstrate the usefulness of our result, we give a new proof of local-in-time existence and uniqueness for the van Roosbroeck system for semiconductor devices which is much simpler than already established proofs.

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