Maximal regularity for evolution equations with critical singular perturbations
Functional Analysis
2026-02-27 v2 Analysis of PDEs
Abstract
Assuming has maximal -regularity, this paper investigates perturbations of by time-dependent operators that are unbounded and satisfy a critical -integrability condition in time. We establish two main results. The first proves maximal -regularity for the critical endpoint case, generalizing previous work by Pr\"uss and Schnaubelt (2001). The second develops a weighted maximal regularity theory for mixed-scale perturbations, motivated by the linearized skeleton equations appearing in large deviations theory for stochastic PDEs.
Cite
@article{arxiv.2602.00895,
title = {Maximal regularity for evolution equations with critical singular perturbations},
author = {Esmée Theewis and Mark Veraar},
journal= {arXiv preprint arXiv:2602.00895},
year = {2026}
}
Comments
Assumption 3.7 relaxed, minor changes in Section 3