Maximal regularity for evolution equations with critical singular perturbations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910033407639552 |
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| author | Theewis, Esmée Veraar, Mark |
| author_facet | Theewis, Esmée Veraar, Mark |
| contents | 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 Prüss 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal regularity for evolution equations with critical singular perturbations Theewis, Esmée Veraar, Mark Functional Analysis Analysis of PDEs 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 Prüss 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. |
| title | Maximal regularity for evolution equations with critical singular perturbations |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2602.00895 |