Hairer's multilevel Schauder estimates without Regularity Structures

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.

60 pages, published version

References in corpus (10)

• A theory of regularity structures
• Renormalising SPDEs in regularity structures
• The continuous Anderson hamiltonian in $d\le 3$
• The reconstruction theorem in Besov spaces
• Fluctuations around a homogenised semilinear random PDE
• Reconstruction Theorem for Germs of Distributions on Smooth Manifolds
• Model Spaces of Regularity Structures for Space-Fractional SPDEs
• Hairer's Reconstruction Theorem without Regularity Structures
• Boundary renormalisation of SPDEs
• The BPHZ Theorem for Regularity Structures via the Spectral Gap Inequality