Allgemeine parabolische Systeme gemischter Ordnung in Lp und Anwendungen

The aim of this thesis is to develop a theory for the treatment of linear parabolic partial differential equations. Here we consider problems on the whole space as well as boundary value problems with dynamic boundary conditions. To be more precise, we establish results about mixed order systems on Lp, which help us to give elegant and short proofs of the well-posedness of linear parabolic problems. For the treatment of non-linear partial differential equations a thorough understanding of the associated linearized problem is indispensable.We treat mixed order systems by a functional calculus of the time and spaces derivatives. This calculus is highly related to the theory of Lp-Fourier multipliers.For the treatment of Lp-Lq problems we establish results on Bessel-valued Triebel-Lizorkin spaces. These spaces are necessary due to the canonically occurrence of them in trace spaces.In the last chapter we present a selection of applications on the whole space and on half-spaces. Especially, we prove the well-posedness of the linearizations of the two-phase Navier-Stokes equations with Boussinesq-Scriven surface and the Lp-Lq two-phase Stefan problem with Gibbs-Thomson correction