Lions' maximal regularity problem with H 1/ 2 -regularity in time
Analysis of PDEs
2017-09-14 v1 Functional Analysis
Abstract
We consider the problem of maximal regularity for non-autonomous Cauchy problems u ' (t) + A(t) u(t) = f (t), t (0, ] 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.
Cite
@article{arxiv.1709.04216,
title = {Lions' maximal regularity problem with H 1/ 2 -regularity in time},
author = {Mahdi Achache and El Maati Ouhabaz},
journal= {arXiv preprint arXiv:1709.04216},
year = {2017}
}