AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS RELATED TO TUG-OF-WAR GAMES

作者：Manfredi Juan J^*; Parviainen Mikko; Rossi Julio D

来源：SIAM Journal on Mathematical Analysis, 2010, 42(5): 2058-2081.

DOI：10.1137/100782073

• Dirichlet boundary conditions
• dynamic programming principle
• parabolic p-Laplacian
• parabolic mean value property
• stochastic games
• tug-of-war games with limited number of rounds
• viscosity solutions

We characterize solutions to the homogeneous parabolic p-Laplace equation u(t) - vertical bar del u|(2-p)Delta(p)u = (p - 2)Delta(infinity)u + Delta u in terms of an asymptotic mean value property. The results are connected with the analysis of tug-of-war games with noise in which the number of rounds is bounded. The value functions for these games approximate a solution to the PDE above when the parameter that controls the size of the possible steps goes to zero.

• 出版日期2010