Special Session 11: Stochastic Partial Differential Equations

The Porous Medium Equation: Multiscale Integrability in Large Deviations
Daniel Heydecker
University of Oslo
Norway
Co-Author(s):    Benjamin Gess
Abstract:
We consider the large deviations of a particle system $\eta^N$ with degenerate and superlinear diffusivity. The key challenge is to develop uniform integrability estimate on the nonlinearity $(\eta^N(x))^\alpha$ in a situation where neither pathwise regularity nor Dirichlet-form based regularity is readily available. This is resolved introducing a novel multiscale argument exploiting the appearance of pathwise regularity across scales.