Meinlschmidt H, Rehberg J (2021)
Publication Type: Journal article
Publication year: 2021
Book Volume: 280
Pages Range: 375-404
DOI: 10.1016/j.jde.2021.01.032
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 XDs−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.
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://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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