presso la Sala Conferenze "F. Tricerri" del Dipartimento di Matematica e Informatica "U. DINI"
Il Prof. Marta Lewicka
(University of Pittsburgh)
terrà una conferenza dal titolo:
"Game theoretical methods in PDEs"
Abstract:
The objective of this lecture is to give a brief self-contained introduction to how random tug-of-war games are applied to gain new proofs and insights in the theory of nonlinear partial differential equations. We first revisit the classical linear case, where an interplay between harmonic functions and martingales is based on a common cancellation property, expressed via the mean value property. We then pass to the nonlinear case and explain the connection between tug-of-war games and the, so called, infinity harmonic functions as established by Peres, Schramm, Sheffield and Wilson in 2009, followed by the case of p-harmonic functions due to Peres and Sheffield and furthered by Manfredi, Parviainen and Rossi in 2011. We shall see how solutions to these and certain other well-known Pdes can be interpreted as values of a game, in the limit when the distance that the token is allowed to be 'tugged' by players in their preferred directions at each turn of the game, decreases to zero.