Non-autonomous maximal regularity under Besov regularity in time
Language
en
Document de travail - Pré-publication
English Abstract
We consider the maximal regularity problem for the non-autonomous Cauchy problems u ′ (t) + A(t)u(t) = f (t) t-a.e., u(0) = u 0. (0.1) In this case, the time dependent operators A(t) are associated with a family of ...Read more >
We consider the maximal regularity problem for the non-autonomous Cauchy problems u ′ (t) + A(t)u(t) = f (t) t-a.e., u(0) = u 0. (0.1) In this case, the time dependent operators A(t) are associated with a family of sesquilinear forms. We prove maximal L p-regularity results with p ≤ 2 under minimal regularity assumptions on the forms. Our main assumption is that (A(t)) t∈[0,τ ] are piecewise in the Besov space B 1 2 ,2 p with respect to the variable t. This regularity assumption is optimal and our result is the most general one.Read less <
English Keywords
Besov space
maximal regularity
mon-autonomous evolution equations
sesquilinear forms. Mathematics Subject Classification (2010): 35K90
35K45
47D06
Origin
Hal imported