Brownian motion and exposed solutions of differential inclusions

Martedi' 6 Marzo 2012 - Giovanni Colombo


Martedi` 6 marzo 2012 alle ore 12:30 in aula 1BC50 Giovanni Colombo (Universita' di Padova) terra' un seminario dal titolo "Brownian motion and exposed solutions of differential inclusions".

We present a research program designed by A. Bressan and some partial results related to it. First, we construct a probability measure supported on the space of solutions to a planar differential inclusion, where the right hand side is a Lipschitz continuous segment. Such measure assigns probability one to solutions having derivatives a.e.~equal to one of the endpoints of the segment. Second, for a class of planar differential inclusions with Holder continuous right hand side F, we prove existence of solutions whose derivatives are exposed points of F. Finally, we complete the research program if the right hand side of the differential inclusion does not depend on the state. The proofs rely on basic properties of the scalar Brownian motion. Joint work with V. Goncharov, with MANY thanks to P. Dai Pra.

Rif. int. M. Bardi, P. Mannucci, C. Marchi

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