The obstacle problem for the p-laplacian via optimal stopping of tug-of-war games

• 成果类型: Article
• 署名作者: Lewicka, Marta; Manfredi, Juan J.
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0684-y
• 发表日期: 2017
• 页码: 349-378
• 关键词: harmonic functions; equation

摘要

We present a probabilistic approach to the obstacle problem for the p-Laplace operator. The solutions are approximated by running processes determined by tug-of-war games plus noise, and letting the step size go to zero, not unlike the case when Brownian motion is approximated by random walks. Rather than stopping the process when the boundary is reached, the value function is obtained by maximizing over all possible stopping times that are smaller than the exit time of the domain.