Boundary renormalisation of SPDEs
Máté Gerencsér, Martin Hairer · Communications in Partial Differential Equations · 2022
We consider the continuum parabolic Anderson model (PAM) and the dynamical Φ4 equation on the 3-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for Φ34 a ‘boundary triviality’ result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.