Nonscalar Parabolic Equations

Abstract

The results on existence of analytic resolvents in Section 2 and on resolvents for parabolic problems in Section 3 as well as the corresponding results on maximal regularity of type C ^α are here extended to nonscalar equations. Particularly easy to verify are the conditions in the variational approach in Section 7.3 which continues the discussion begun in Section 6.7. The remaining subsections are devoted to a far reaching improvement of the perturbation theorem from Section 6.3 in the parabolic case.