THE STEFAN PROBLEM AND FREE TARGETS OF OPTIMAL BROWNIANMARTINGALE TRANSPORT

• 成果类型: Article
• 署名作者: Kim, Inwon C.; Kim, Young-Heon
• 署名单位: University of California System; University of California Los Angeles; University of British Columbia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2026
• 发表日期: 2024
• 页码: 2364-2414
• 关键词: free-boundary; hele-shaw; stopping-times; roots barrier; REGULARITY; EXISTENCE; MODEL

摘要

e formulate and solve a free target optimal Brownian stopping prob-lem from a given distribution while the target distribution is free and is con-ditioned to satisfy a given density height constraint. The free target optimiza-tion problem exhibits monotonicity, from which a remarkable universalityfollows, in the sense that the optimal target is independent of its Lagrangiancost type. In particular, the solutions to this optimization problem generatesolutions to both unstable and stable type of the Stefan problem, where theformer stands for freezing of supercooled fluid(St1)and the latter for icemelting(St2). This unified approach to both types of the Stefan problem isnew. In particular we obtain global-time existence and weak-strong unique-ness for the ill-posed freezing problem(St1), for a given initial data and for awell-prepared class of initial domains generated from the initial data