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

Meinlschmidt H, Rehberg J (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Journal of Differential Equations Elsevier

Book Volume: 280

Pages Range: 375-404

DOI: 10.1016/j.jde.2021.01.032

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 XD^s−1,q(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.

Authors with CRIS profile

Hannes Meinlschmidt

Involved external institutions

Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V.

Germany (DE) Johann Radon Institute

Austria (AT)

How to cite

APA:

Meinlschmidt, H., & Rehberg, J. (2021). Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations. Journal of Differential Equations, 280, 375-404. https://dx.doi.org/10.1016/j.jde.2021.01.032

MLA:

Meinlschmidt, Hannes, and Joachim Rehberg. "Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations." Journal of Differential Equations 280 (2021): 375-404.

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