Juan J. Manfredi (University of Pittsburgh).
Título: Nonlinear mean values.
Abstract: The classical mean value property characterizes harmonic functions. It can be extended to many linear equations. We will focus instead on when it can be extended, albeit in some weaker asymptotic form, to characterize solutions of nonlinear equations. This question has been partially motivated by the connection between Random Tug-of-War games and the normalized p-Laplacian equation discovered some years ago, where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. Our goal is to show that an asymptotic nonlinear mean value formula holds for several types of non-linear equations, including the classical Monge-Ampère equation.
Based on joint work with Pablo Blanc (Jyväskylä), Fernando Charro (Detroit), and Julio Rossi (Buenos Aires).
Massimo Grossi (Università La Sapienza di Roma).
Título: On the number of critical points of solutions of PDE.
Abstract: ver adjunto.