Translator Disclaimer
MArch/April 2009 A billiard-based game interpretation of the Neumann problem for the curve shortening equation
Yoshikazu Giga, Qing Liu
Adv. Differential Equations 14(3/4): 201-240 (MArch/April 2009).

Abstract

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.

Citation

Download Citation

Yoshikazu Giga. Qing Liu. "A billiard-based game interpretation of the Neumann problem for the curve shortening equation." Adv. Differential Equations 14 (3/4) 201 - 240, MArch/April 2009.

Information

Published: MArch/April 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1170.35437
MathSciNet: MR2493561

Subjects:
Primary: 35K20, 49L25, 53C44, 91A05

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
40 PAGES


SHARE
Vol.14 • No. 3/4 • MArch/April 2009
Back to Top