Hairer's multilevel Schauder estimates without Regularity Structures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910621658775552 |
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| author | Broux, Lucas Caravenna, Francesco Zambotti, Lorenzo |
| author_facet | Broux, Lucas Caravenna, Francesco Zambotti, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07517 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hairer's multilevel Schauder estimates without Regularity Structures Broux, Lucas Caravenna, Francesco Zambotti, Lorenzo Analysis of PDEs Probability 46F10 (Primary), 60L30 (Secondary) 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. |
| title | Hairer's multilevel Schauder estimates without Regularity Structures |
| topic | Analysis of PDEs Probability 46F10 (Primary), 60L30 (Secondary) |
| url | https://arxiv.org/abs/2301.07517 |