A new approach to regularity structures is developed and applied in the context of quasi-linear singular SPDEs.  Renormalization counter-terms are identified and a priori estimates are obtained in the full sub-critical regime of roughness of the noise.  In a separate expository note, we also give a short and accessible proof of a key ingredient for the a priori bounds: a generalized Schauder type estimate used in the analysis of the SPDE.

Publication:

1.  Felix Otto, Jonas Sauer, Scott A. Smith, Hendrik Weber, A priori bounds for quasi-linear SPDEs in the full subcritical regime. Journal of the European Mathematical Society 27 (2025), no. 1, pp. 71–118

2. Jonas Sauer, Scott A. Smith, Schauder estimates for germs by scaling. Stochastic PDE:Analysis and Computations, Special Issue In Memory of Giuseppe Da Prato (2025)

Author:

Felix Otto

Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany

felix.otto@mis.mpg.de

Jonas Sauer

Faculty of Mathematics and Computer Science, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany

jonas.sauer@uni-jena.de

Scott A. Smith (corresponding author)

Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, P. R. China;

ssmith@amss.ac.cn

Hendrik Weber

Faculty of Mathematics and Computer Science, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany

hendrik.weber@uni-muenster.de