Abstracts - Facultatea de Matematică

Invited Speakers
Variational Methods in Metric Regularity and Implicit
Multifunction Theorems
D. AZÉ
UMR CNRS MIP, Université Paul Sabatier
118 Route de Narbonne, 31062 Toulouse cedex 4, France
aze@mip.ups-tlse.fr
Relying on the notion of strong slope introduced by De Giorgi, Marino and Tosques
in the eighties, we develop a general framework leading to several characterizations of
metric regularity of multifunctions in the complete metric space setting. We focus our
attention on parametric metric regularity, leading to implicit multifunction theorems.
We give several results on existence and regularity of the implicit multifunctions, and,
surveying some recent results on this topic, we show how they can be derived from
our general method. We also give an exact formula for the derivative of the implicit
multifunction. At last, some applications are given to differential inclusions and to
stability in nonsmooth analysis.
Stochastic Taylor expansion and stochastic viscosity solutions
for nonlinear SPDEs
Rainer BUCKDAHN
Université de Bretagne Occidentale, UFR Sciences et Techniques
Laboratoire de Mathématiques, CNRS - UMR 6204
buckdahn@univ-brest.fr
In an earlier work R.Buckdahn and J.Ma (2001) introduced a notion of stochastic
viscosity solution, inspired by earlier results of P.L.Lions and P.E.Souganidis (1998). By
using a Doss-Sussmann-type transformation and the so-called backward doubly stochastic
differential equations (BDSDEs) introduced by E.Pardoux and S.Peng (1994), they
established the existence and uniqueness of stochastic viscosity solution to the stochastic
partial differential equation (SPDE)
u(t, x) = u(0, x) + � t
g(t, x, u(t, x))dBt,
0 (Au + f(x, u, σ∗∇u) (t, x)dt + � t
0
where B is a Brownian motion and A is the generator of a diffusion process. Our
contribution extends the study of stochastic viscosity solutions to the class of SPDEs
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