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/10.34657/3216https://oa.tib.eu/renate/handle/123456789/3223In 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.application/pdfeng510Evolution equationsmonotone operatorssecond order parabolic boundary value problemsinstationary drift-diffusion problemsnonsmooth coefficientsmixed boundary conditionsLipschitz domainsLipschitz hypersurfacesregular setsMorrey– Campanato spacesSobolev–Morrey spacesPoincar´e inequalitiesReport