Electronic Journal of Differential Equations (Dec 2020)

Maximal regularity for non-autonomous Cauchy problems in weighted spaces

  • Achache Mahdi,
  • Tebbani Hossni

Journal volume & issue
Vol. 2020, no. 124,
pp. 1 – 24

Abstract

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We consider the regularity for the non-autonomous Cauchy problem $$ u'(t) + A(t) u(t) = f(t)\quad (t \in [0, \tau]), \quad u(0) = u_0. $$ The time dependent operator A(t) is associated with (time dependent) sesquilinear forms on a Hilbert space $\mathcal{H}$. We prove the maximal regularity result in temporally weighted L^2-spaces and other regularity properties for the solution of the problem under minimal regularity assumptions on the forms and the initial value u_0. Our results are motivated by boundary value problems.

Keywords