The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content

SPD

Seminar

Stochastic variational inequalities and applications to the total variation flow pertubed by linear multiplicative noise

Röckner, M (Universität Bielefeld)
Friday 14 September 2012, 09:50-10:40

Seminar Room 1, Newton Institute

Abstract

We extend the approach of variational inequalities (VI) to partial differential equations (PDE) with singular coefficients, to the stochastic case. As a model case we concentrate on the parabolic 1-Laplace equation (a PDE with highly singular diffusivity) on a bounded convex domain in N-dimensional Euclidean space, perturbed by linear multiplicative noise, where the latter is given by a function valued (infinite dimensional) Wiener process. We prove existence and uniqueness of solutions for the corresponding stochastic variational inequality (SVI) in all space dimensions N and for any square-integrable initial condition, thus obtaining a stochastic version of the (minimal) total variation flow. One main tool to achieve this, is to transform the SVI and its approximating stochastic PDE into a deterministic VI, PDE respectively, with random coefficients, thus gaining sharper spatial regularity results for the solutions. We also prove finite time extinction of solutions with positive probability in up to N = 3 space dimensions.

Presentation

[pdf ]

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧