A Billiard-Based Game Interpretation of the Neumann Problem for the Curve Shortening Equation

Giga Yoshikazu, Liu Qing

doi:10.14943/84071

A Billiard-Based Game Interpretation of the Neumann Problem for the Curve Shortening Equation

DOI 機関リポジトリ (HANDLE) オープンアクセス

書誌事項

公開日: 2008

資源種別: departmental bulletin paper

DOI

10.14943/84071

公開者: Department of Mathematics, Hokkaido University

説明

This paper constructs a family of discrete games, whose value functions converge to the unique viscosity solution of the Neumann boundary problem of the curve shortening flow equation. To derive the boundary condition, a billiard semiflow is introduced and its basic properties near the boundary are studied for convex and more general domains. It turns out that Neumann boundary problems of mean curvature flow equations can be intimately connected with purely deterministic game theory.

収録刊行物

Hokkaido University Preprint Series in Mathematics

Hokkaido University Preprint Series in Mathematics 922 1-40, 2008

Department of Mathematics, Hokkaido University