Regularity for evolution equations with non-autonomous perturbations in Banach spaces

Abstract

We provide regularity of solutions to a large class of evolution equations on Banach spaces where the generator is composed of a static principal part plus a non-autonomous perturbation. Regularity is examined with respect to the graph norm of the iterations of the principal part. The results are applied to the Schrödinger equation and conditions on a time-dependent scalar potential for regularity of the solution in higher Sobolev spaces are derived.

References in corpus (4)

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Cited by in corpus (4)

• A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density
• Towards a mathematical Theory of the Madelung Equations
• Convergence Rates for the Trotter Splitting for Unbounded Operators
• On the applicability of Kolmogorov's theory of probability to the description of quantum phenomena. Part I: foundations