A Deterministic Game-Theoretic Approach to Convexity-Preserving Property and Finite-Time Extinction of Level Sets for Geometric Equations

We consider the convexity-preserving property and finite-time extinction of level sets for quasilinear geometric equations using a game-theoretic approach introduced by Kohn and Serfaty. To construct the game whose value function approximates the viscosity solution, we use the approach introduced by Sato.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34671
Primary Topic
Nonlinear Partial Differential Equations
Type
preprint
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preprint

A Deterministic Game-Theoretic Approach to Convexity-Preserving Property and Finite-Time Extinction of Level Sets for Geometric Equations

Kazuhiro Takimoto, Yousuke Saga
arXiv (Cornell University)
Nonlinear Partial Differential Equations
preprint

A Deterministic Game-Theoretic Approach to Convexity-Preserving Property and Finite-Time Extinction of Level Sets for Geometric Equations

Kazuhiro Takimoto, Yousuke Saga
preprint en

Abstract

We consider the convexity-preserving property and finite-time extinction of level sets for quasilinear geometric equations using a game-theoretic approach introduced by Kohn and Serfaty. To construct the game whose value function approximates the viscosity solution, we use the approach introduced by Sato.

arXiv (Cornell University)
Nonlinear Partial Differential Equations
DOIOpen Access PDFOpenAlex
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A Deterministic Game-Theoretic Approach to Convexity-Preserving Property and Finite-Time Extinction of Level Sets for Geometric Equations — Kazuhiro Takimoto, Yousuke Saga · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS