WIAS Preprint No. 1083, (2005)

Sobolev-Morrey spaces associated with evolution equations



Authors

  • Griepentrog, Jens André

2010 Mathematics Subject Classification

  • 35D10 35R05 35K90

Keywords

  • Evolution equations, monotone operators, second order parabolic bondary value problems, instationary drift-diffusion problems, nonsmooth coefficients, mixed boundary conditions, LIPSCHITZ domains, LIPSCHITZ hypersurfaces, regular sets, MORREY-CAMPANATO spaces, SOBOLEV-MORREY spaces, POINCARE inequalities

Abstract

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 greater or equal than three 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 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.

Appeared in

  • Adv. Differential Equations, 12 (2007) pp. 781--840.

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