Noisy tug of war games for the $p$-Laplacian: 1 < p < $\infty$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1512/IUMJ.2021.70.8358

M. Lewicka

引用次数: 2

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吵吵闹闹的拔河游戏$p$ -拉普拉斯:1 < p < $\infty$

。针对N维域上的齐次p -拉普拉斯方程，结合带噪声的拔河游戏，提出了Dirichlet问题的一种新的有限差分近似。我们的游戏和我们开发的相关均值展开，将球上的“确定性平均值”“12 (inf + sup)”与N维椭球上的“随机平均值”“ffl”叠加在一起，这些椭球的纵横比取决于N, p，并且在确定inf / sup时方向跨越所有方向。我们证明了相关动态规划原理的唯一解u (cid:15)对于连续边界数据是自动连续的。并与明确定义的游戏价值相一致。因此，我们的游戏具有最小-最大属性:将结果凌驾于一方策略之上，将结果凌驾于对手策略之上的顺序是无关紧要的。进一步证明了满足外部螺旋条件的域在这种情况下是博弈正则的，即族{u (cid:15)} (cid:15)→0一致收敛于Dirichlet问题的唯一粘性解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.