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<p>We consider the free boundary problems of degenerate elliptic equations that describe the level set formulation of the interface motion evolved by anisotropic forced mean curvature flow. We develop a deterministic game representation for our equations based on a discrete approximation scheme proposed by Kohn and Serfaty and establish the comparison principle for our free boundary problems. Since the standard doubling variable methods in the theory of viscosity solutions do not work for the free boundary problems, we prove the comparison principle by using the game approximation.</p>

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A game approach to free boundary problems of anisotropic forced mean curvature flow equations

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Takuya Sato

摘要

We consider the free boundary problems of degenerate elliptic equations that describe the level set formulation of the interface motion evolved by anisotropic forced mean curvature flow. We develop a deterministic game representation for our equations based on a discrete approximation scheme proposed by Kohn and Serfaty and establish the comparison principle for our free boundary problems. Since the standard doubling variable methods in the theory of viscosity solutions do not work for the free boundary problems, we prove the comparison principle by using the game approximation.