Regularity for degenerate evolution equations with strong absorption

Regularity Results for Very Degenerate Elliptic Equations

We consider a family of elliptic equations introduced in the context of traffic congestion. They have the form ∇·(∇F(∇u)) = f , where F is a convex function which vanishes inside some convex set and is elliptic outside. Under some natural assumptions on F and f , we prove that the function ∇F(∇u) is continuous in any dimension, extending a previous result valid only in dimension 2 [14]. Résumé....

Maximal Regularity for Evolution Equations

A Strong Regularity Result for Parabolic Equations

We consider a parabolic equation with a drift term u+b∇u−ut = 0. Under the condition divb = 0, we prove that solutions possess dramatically better regularity than those provided by standard theory. For example, we prove continuity of solutions when not even boundedness is expected.

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

Maximal regularity for nonautonomous evolution equations

We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity. 1991 Mathematics Subject Classification. 35K90, 47D06.