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

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

A multiplicity result for a class of elliptic boundary value problems

We consider a mildly nonlinear elliptic boundary value problem depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we derive lower bounds on the number of solutions. The results complement an earlier theorem due to Kazdan and Warner [6

Compact embeddings of vector valued Sobolev and Besov spaces

The main result of this paper is a generalization and sharpening of the Aubin-Dubinskii lemma concerning compact subsets in vector-valued Lebesque spaces. In addition, there are given some new embedding results for vector valued Besov spaces

A multiplicity result for a class of elliptic boundary value problems

SynopsisWe consider a mildly nonlinear elliptic boundary value problem depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we derive lower bounds on the number of solutions. The results complement an earlier theorem due to Kazdan and Warner [6]