Lions' maximal regularity problem with H 1/ 2 -regularity in time
Idioma
en
Article de revue
Este ítem está publicado en
Journal of Differential Equations. 2019
Elsevier
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
47D06
non-autonomous evolution equations
Maximal regularity
Sobolev regularity
Mathematics Subject Classification (2010): 35K90
35K45
Orígen
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