Homogenization of degenerate cross-diffusion systems

Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic het...

Homogenization of periodic linear degenerate PDEs

It is well-known under the name of ‘periodic homogenization’ that, under a centering condition of the drift, a periodic diffusion process on R converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of this result all rely on uniform ellipticity or hypoellipticity assumptions on the diffusion. In this paper, we considerably weaken these assumptions in order to ...

Homogenization of periodic semilinear parabolic degenerate PDEs

In this paper a second order semilinear parabolic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some part of Rd . Our fully probabilistic method is based on the deep connection between PDEs and BSDEs and the weak convergence of a class of diffusion processe...

Quantitative Homogenization of Global Attractors For Reaction-Diffusion Systems . . .

The Regularity of General Parabolic Systems with Degenerate Diffusion

The aim of the talk is twofold. On one hand we want to present a new technique called p-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classica...