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Motion of a Graph by R-Curvature

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Abstract.

We show the existence of weak solutions to the partial differential equation which describes the motion by R-curvature in R d, by the continuum limit of a class of infinite particle systems. We also show that weak solutions of the partial differential equation are viscosity solutions and give the uniqueness result on both weak and viscosity solutions.

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Authors and Affiliations

  1. Department of Mathematics, School of Education Waseda University, 1-6-1 Nishiwaseda, Shinjyuku-ku, Tokyo, 169-8050, Japan

    Hitoshi Ishii

  2. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Toshio Mikami

Authors
  1. Hitoshi Ishii
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  2. Toshio Mikami
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Communicated by P.-L. Lions

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Ishii, H., Mikami, T. Motion of a Graph by R-Curvature. Arch. Rational Mech. Anal. 171, 1–23 (2004). https://doi.org/10.1007/s00205-003-0294-1

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  • DOI: https://doi.org/10.1007/s00205-003-0294-1

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