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SUMMARY:Stochastic variational inequalities and applications to the total 
 variation flow pertubed by linear multiplicative noise - Rckner\, M (Unive
 rsitt Bielefeld)
DTSTART:20120914T085000Z
DTEND:20120914T094000Z
UID:TALK39749@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We extend the approach of variational inequalities (VI) to par
 tial differential equations (PDE) with singular coefficients\, to the stoc
 hastic case. As a model case we concentrate on the parabolic 1-Laplace equ
 ation (a PDE with highly singular diffusivity) on a bounded convex domain 
 in N-dimensional Euclidean space\, perturbed by linear multiplicative nois
 e\, where the latter is given by a function valued (infinite dimensional) 
 Wiener process. We prove existence and uniqueness of solutions for the cor
 responding stochastic variational inequality (SVI) in all space dimensions
  N and for any square-integrable initial condition\, thus obtaining a stoc
 hastic version of the (minimal) total variation flow. One main tool to ach
 ieve this\, is to transform the SVI and its approximating stochastic PDE i
 nto a deterministic VI\, PDE respectively\, with random coefficients\, thu
 s gaining sharper spatial regularity results for the solutions. We also pr
 ove finite time extinction of solutions with positive probability in up to
  N = 3 space dimensions.\n
LOCATION:Seminar Room 1\, Newton Institute
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