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Author: Griepentrog, Jens A. × Subject: mixed boundary conditions ×

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    Sobolev-Morrey spaces associated with evolution equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Griepentrog, Jens A.
    In this text we introduce new classes of Sobolev-Morrey spaces being adequate for the regularity theory of second order parabolic boundary value problems on Lipschitz domains of space dimension n ≥ 3 with nonsmooth coefficients and mixed boundary conditions. We prove embedding and trace theorems as well as invariance properties of these spaces with respect to localization, Lipschitz transformation, and reflection. In the second part [11] of our presentation we show that the class of second order parabolic systems with diagonal principal part generates isomorphisms between the above mentioned Sobolev-Morrey spaces of solutions and right hand sides.
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    Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Griepentrog, Jens A.
    This text is devoted to maximal regularity results for second order parabolic systems on Lipschitz domains of space dimension n ≥ 3 with diagonal principal part, nonsmooth coefficients, and nonhomogeneous mixed boundary conditions. We show that the corresponding class of initial boundary value problems generates isomorphisms between two scales of Sobolev–Morrey spaces for solutions and right hand sides introduced in the first part [12] of our presentation. The solutions depend smoothly on the data of the problem. Moreover, they are Hölder continuous in time and space up to the boundary for a certain range of Morrey exponents. Due to the complete continuity of embedding and trace maps these results remain true for a broad class of unbounded lower order coefficients.