Parabolic equations on uniformly regular Riemannian manifolds and degenerate initial boundary value problems

Abstract

In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying approach to problems with strong degeneracies in the interior or at the boundary.Comment: To appear in "Recent Developments of Mathematical Fluid Mechanics", Series: Advances in Mathematical Fluid Mechanics, Birkhaeuser-Verlag, Editors: G. P. Galdi, J. G. Heywood and R. Rannacher. Some misprints of the earlier version have been correcte