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arXiv · 2301.07517

Hairer's multilevel Schauder estimates without Regularity Structures

Lucas Broux·Francesco Caravenna·Lorenzo Zambotti
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Abstract

We investigate the regularising properties of singular kernels at the level of germs, i.e. families of distributions indexed by points in $\mathbb{R}^d$. First we construct a suitable integration map which acts on general coherent germs. Then we focus on germs that can be decomposed along a basis (corresponding to the so-called modelled distributions in Regularity Structures) and we prove a version of Hairer's multilevel Schauder estimates in this setting, with minimal assumptions.

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Lucas Broux, Francesco Caravenna, Lorenzo Zambotti. 2023-01-18. Hairer's multilevel Schauder estimates without Regularity Structures. https://doi.org/10.1090/tran/9245

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