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A Comparison Principle for the Mean Curvature Flow Equation with Discontinuous Coefficients

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  • Cecilia De Zan
  • Pierpaolo Soravia

Abstract

We study the level set equation in a bounded domain when the velocity of the interface is given by the mean curvature plus a discontinuous velocity. We prove a comparison principle for the initial-boundary value problem whose consequence is uniqueness of continuous solutions and well- posedness of the level set method.

Suggested Citation

  • Cecilia De Zan & Pierpaolo Soravia, 2016. "A Comparison Principle for the Mean Curvature Flow Equation with Discontinuous Coefficients," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-6, August.
    • Handle: RePEc:hin:jnijde:3627896
    DOI: 10.1155/2016/3627896
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    Cited by:

    1. Yoshikazu Giga & Norbert Požár, 2020. "Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term," Partial Differential Equations and Applications, Springer, vol. 1(6), pages 1-26, December.

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