Optimal Regularity for a Class of Singular Abstract Parabolic Equations

Details Optimal Regularity for a Class of Singular Abstract Parabolic Equations Optimal Regularity for a Class of Singular Abstract Parabolic Equations

2006-10-26

arxiv.org/abs/math/0610797v1

Mathematics

Analysis of PDEs

Scientific paper

A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is subsequently used to derive optimal regularity results. The latter are well known to be important basic tools needed to deal with corresponding nonlinear Cauchy Problems such as those associated to Free Boundary Problems.

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