Schauder Estimates for Germs by Scaling

TL;DR

This paper demonstrates how blow-up arguments from classical PDE theory can be adapted to Schauder estimates for germs in singular SPDEs, emphasizing the role of scaling and Liouville principles.

Contribution

It introduces a method to apply classical blow-up techniques to the Schauder theory of germs in the context of singular SPDEs, bridging PDE and stochastic analysis.

Findings

Blow-up arguments effectively adapt to germ Schauder estimates.

Scaling properties are crucial for the analysis.

Liouville principles underpin the theoretical framework.

Abstract

In this expository note, we show that the blow-up arguments of L. Simon adapt well to the corresponding Schauder theory of germs used in the study of singular SPDEs. We illustrate this through some representative examples. As in the classical PDE framework, the argument relies only on the scaling properties of the germ semi-norms and the Liouville principle for the operator.