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arXiv · 2602.00895

Maximal regularity for evolution equations with critical singular perturbations

Esmée Theewis·Mark Veraar
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Abstract

Assuming $A$ has maximal $L^p$-regularity, this paper investigates perturbations of $A$ by time-dependent operators $B$ that are unbounded and satisfy a critical $L^q$-integrability condition in time. We establish two main results. The first proves maximal $L^p$-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.

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Esmée Theewis, Mark Veraar. 2026-01-31. Maximal regularity for evolution equations with critical singular perturbations. https://arxiv.org/abs/2602.00895

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