A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate
Analysis of PDEs
2025-01-23 v2 Probability
Abstract
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].
Keywords
Cite
@article{arxiv.2310.07396,
title = {A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate},
author = {Masato Hoshino},
journal= {arXiv preprint arXiv:2310.07396},
year = {2025}
}