Lions' maximal regularity problem with H 1/ 2 -regularity in time
Language
en
Article de revue
This item was published in
Journal of Differential Equations. 2019
Elsevier
English Abstract
We consider the problem of maximal regularity for non-autonomous Cauchy problems u ′ (t) + A(t) u(t) = f (t), t ∈ (0, τ ] u(0) = u 0. The time dependent operators A(t) are associated with (time dependent) sesquilinear forms ...Read more >
We consider the problem of maximal regularity for non-autonomous Cauchy problems u ′ (t) + A(t) u(t) = f (t), t ∈ (0, τ ] u(0) = u 0. The time dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space H. We are interested in J.L. Lions's problem concerning maximal regularity of such equations. We give a positive answer to this problem under minimal regularity assumptions on the forms. Our main assumption is that the forms are piecewise H 1 2 with respect to the variable t. This regularity assumption is optimal and our results are the most general ones on this problem.Read less <
English Keywords
47D06
non-autonomous evolution equations
Maximal regularity
Sobolev regularity
Mathematics Subject Classification (2010): 35K90
35K45
Origin
Hal imported