Regularity for evolution equations with non-autonomous perturbations in Banach spaces
Mathematical Physics
2018-11-02 v3 Analysis of PDEs
math.MP
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.
Cite
@article{arxiv.1801.03361,
title = {Regularity for evolution equations with non-autonomous perturbations in Banach spaces},
author = {Markus Penz},
journal= {arXiv preprint arXiv:1801.03361},
year = {2018}
}