Optimal Regularity for a Class of Singular Abstract Parabolic Equations

Abstract

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.

References in corpus (1)

• A Class of Free Boundary Problems with Onset of a new Phase

Cited by in corpus (3)

• The Cauchy problem for operator-Boussinesq equations
• Morgan type uncertainty principle and unique continuation properties for abstract Schrödinger equations
• Unique continuation properties for abstract Schroedinger equations and applications