The flow approach to SPDEs with boundary conditions

Abstract: We will discuss how to study renormalisation of Stochastic PDEs in the presence of Boundary conditions, using the flow approach introduced by Pawel Duch. In particular we look at the $\Phi^4$ equation with Dirichlet boundary conditions on a general domain with smooth boundary. We find the need for additional renormalisation accounting for the boundary conditions, as in previous work of Gerencer and Hairer. We show that this boundary renormalisation can be taken constant even for domains with curved boundary. This is joint work with Majdouline Borji and Leonard Ferdinand.

MathematicsPhysics

Audience: researchers in the topic

Probability, Statistical Mechanics and Quantum Fields

Series comments: Paweł Duch (EPFL) will give a mini-course on "Singular Stochastic PDEs", in the period March 9-20, 2026. Further information can be found here: www.math.sissa.it/course/phd-course/singular-stochastic-pdes. You can follow the course online here: sissa-it.zoom.us/j/84337146226?pwd=SMrOupIjXvQ2pwrc6djLExOCKZPbKZ.1. Please email Ilya Chevyrev for the Zoom passcode.