ar X iv : 0 90 4 . 26 45 v 1 [ m at h . C A ] 1 7 A pr 2 00 9 FOKKER - PLANCK EQUATION IN BOUNDED DOMAIN by Laurent CHUPIN

ar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

Fokker-Planck equation in bounded domain

We study the existence and the uniqueness of a solution φ to the linear Fokker-Planck equation −∆φ+ div(φF) = f in a bounded domain of R when F is a “confinement” vector field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows. Equation de Fokker-Planck dans un domaine b...

ar X iv : 0 70 4 . 01 15 v 2 [ m at h . G T ] 9 A pr 2 00 7 Smooth maps with singularities of bounded K - codimensions ∗ † Yoshifumi ANDO

ar X iv : 0 90 4 . 23 13 v 1 [ m at h . FA ] 1 5 A pr 2 00 9 A DISCRETIZED APPROACH TO W . T . GOWERS ’ GAME

We give an alternative proof of W.T. Gowers' theorem on block bases in Banach spaces by reducing it to a discrete analogue on specific count-able nets.

ar X iv : 0 90 4 . 09 09 v 1 [ m at h . FA ] 6 A pr 2 00 9 On Sobolev extension domains in R

We describe a class of Sobolev W k p -extension domains Ω ⊂ R n determined by a certain inner subhyperbolic metric in Ω. This enables us to characterize finitely connected Sobolev W 1 p -extension domains in R 2 for each p > 2 .