Optimal regularity for a class of singular abstract parabolic equations
Copyright policy )Optimal regularity for a class of singular abstract parabolic equations
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.
- University of California System United States
- University of California, Irvine United States
- University of California, San Francisco United States
Evolution operator, Abstract parabolic equations, One-parameter semigroups and linear evolution equations, Smoothness and regularity of solutions to PDEs, optimal regularity, 35A05, 35K10, 35K65, Mathematics - Analysis of PDEs, Initial-boundary value problems for second-order parabolic equations, singular parabolic initial boundary value problems, FOS: Mathematics, Free boundary problems for PDEs, Optimal regularity, evolution operator, Singular parabolic initial boundary value problems, Analysis, Analysis of PDEs (math.AP)
Evolution operator, Abstract parabolic equations, One-parameter semigroups and linear evolution equations, Smoothness and regularity of solutions to PDEs, optimal regularity, 35A05, 35K10, 35K65, Mathematics - Analysis of PDEs, Initial-boundary value problems for second-order parabolic equations, singular parabolic initial boundary value problems, FOS: Mathematics, Free boundary problems for PDEs, Optimal regularity, evolution operator, Singular parabolic initial boundary value problems, Analysis, Analysis of PDEs (math.AP)
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