On the maximal Lp-regularity of parabolic mixed order systems
R. Denk and J. Seiler
Abstract. We study maximal Lp-regularity for a class of pseudodifferential mixed order systems on a space-time cylinder ℝn x ℝ or X x ℝ where X is a closed smooth manifold. To this end we construct a calculus of Volterra pseudodifferential operators and characterize the parabolicity of a system by the invertibility of certain associated symbols. A parabolic system is shown to induce isomorphisms between suitable Lp-Sobolev spaces of Bessel potential or Besov type. If the cross section of the space-time cylinder is compact, the inverse of a parabolic system belongs to the calculus again. As applications we discuss time-dependent Douglis-Nirenberg systems and a linear system arising in the study of the Stefan problem with Gibbs-Thomson correction.conditions.
J. Evol. Equ. 11 (2011), 371 - 404
DOI 10.1007/s00028-010-0095-6
The paper is available here: (Preprint version).