A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909463458349056 |
|---|---|
| author | Hoshino, Masato |
| author_facet | Hoshino, Masato |
| contents | The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators. Essentially, we use only the semigroup property and the upper estimates of kernels. Moreover, we refine the several types of Besov reconstruction theorems [18, 7] and introduce the new framework "regularity-integrability structures". The analytic theorems in this paper are applied to the study of quasilinear SPDEs [5] and an inductive proof of the convergence of random models [4]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate Hoshino, Masato Analysis of PDEs Probability 46F10, 60L30 The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators. Essentially, we use only the semigroup property and the upper estimates of kernels. Moreover, we refine the several types of Besov reconstruction theorems [18, 7] and introduce the new framework "regularity-integrability structures". The analytic theorems in this paper are applied to the study of quasilinear SPDEs [5] and an inductive proof of the convergence of random models [4]. |
| title | A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate |
| topic | Analysis of PDEs Probability 46F10, 60L30 |
| url | https://arxiv.org/abs/2310.07396 |