This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Griepentrog, Jens A.2016-12-162019-06-2820070946-8633https://doi.org/10.34657/2648https://oa.tib.eu/renate/handle/123456789/3227This 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.application/pdfeng510Second order parabolic boundary value problemsinstationary driftdiffusion problemsnonsmooth coefficientsunbounded lower order coefficientsmixed boundary conditionsLipschitz domainsregular setsHarnack-type inequalityglobal H¨older continuitymaximal regularitySobolev–Morrey spacessmooth dependence of solutionsReport