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

TL;DR

This paper studies the regularity of solutions to evolution equations in Banach spaces with non-autonomous perturbations, applying results to Schrödinger equations to establish higher Sobolev space regularity under certain conditions.

Contribution

It introduces new regularity results for evolution equations with non-autonomous perturbations in Banach spaces, including applications to Schrödinger equations.

Findings

Regularity of solutions in Banach spaces is established.

Conditions for higher Sobolev space regularity in Schrödinger equations are derived.

The approach uses the graph norm of the principal part's iterations.

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 Schr\"odinger equation and conditions on a time-dependent scalar potential for regularity of the solution in higher Sobolev spaces are derived.