Maximal parabolic regularity for divergence operators including mixed boundary conditions. (English) Zbl 1178.35210

Haller-Dintelmann, Robert; Rehberg, Joachim

J. Differ. Equations 247, No. 5, 1354-1396 (2009).

The authors consider operators in divergence form with discontinuous coefficients, satisfying mixed boundary conditions. The main tools of this paper are maximal parabolic regularity techniques and the fact that if a domain is the image under a volume preserving and bi-Lipschitz mapping of Gröger’s model sets, then the maximal regularity property holds. By using these powerful instruments the authors develop a theory that has applications to quasilinear equations with non-smooth data.

Reviewer: Vincenzo Vespri (Firenze)

MSC:

35K59	Quasilinear parabolic equations
35B65	Smoothness and regularity of solutions to PDEs
35R05	PDEs with low regular coefficients and/or low regular data
35K20	Initial-boundary value problems for second-order parabolic equations

Keywords:

mixed Dirichlet-Neumann conditions, Gröger’s model sets; discontinuous coefficients

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