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

Penz, M.

doi:10.1063/1.5011306

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Journal Article

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

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Penz, M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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https://dx.doi.org/10.1063/1.5011306
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https://arxiv.org/abs/1801.03361
(Preprint)

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1.5011306.pdf
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1801.03361.pdf
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Citation

Penz, M. (2018). Regularity for evolution equations with non-autonomous perturbations in Banach spaces. Journal of Mathematical Physics, 59(10): 103512. doi:10.1063/1.5011306.

Cite as: https://hdl.handle.net/21.11116/0000-0002-7FF2-F

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 the regularity of the solution in higher Sobolev spaces are derived.