### Abstract

We construct a discrete stochastic approximation of a convexified Gauss curvature flow of boundaries of bounded open sets in an anisotropic external field. We also show that a weak solution to the PDE which describes the motion of a bounded open set is unique and is a viscosity solution of it.

Original language | English |
---|---|

Pages (from-to) | 552-579 |

Number of pages | 28 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 36 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 |

### Fingerprint

### Keywords

- Convexified Gauss curvature flow
- Stochastic approximation
- Viscosity solution
- Weak solution

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics
- Numerical Analysis

### Cite this

*SIAM Journal on Mathematical Analysis*,

*36*(2), 552-579. https://doi.org/10.1137/S0036141002420509

**Convexified Gauss curvature flow of sets : A stochastic approximation.** / Ishii, Hitoshi; Mikami, Toshio.

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis*, vol. 36, no. 2, pp. 552-579. https://doi.org/10.1137/S0036141002420509

}

TY - JOUR

T1 - Convexified Gauss curvature flow of sets

T2 - A stochastic approximation

AU - Ishii, Hitoshi

AU - Mikami, Toshio

PY - 2005

Y1 - 2005

N2 - We construct a discrete stochastic approximation of a convexified Gauss curvature flow of boundaries of bounded open sets in an anisotropic external field. We also show that a weak solution to the PDE which describes the motion of a bounded open set is unique and is a viscosity solution of it.

AB - We construct a discrete stochastic approximation of a convexified Gauss curvature flow of boundaries of bounded open sets in an anisotropic external field. We also show that a weak solution to the PDE which describes the motion of a bounded open set is unique and is a viscosity solution of it.

KW - Convexified Gauss curvature flow

KW - Stochastic approximation

KW - Viscosity solution

KW - Weak solution

UR - http://www.scopus.com/inward/record.url?scp=14944371769&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14944371769&partnerID=8YFLogxK

U2 - 10.1137/S0036141002420509

DO - 10.1137/S0036141002420509

M3 - Article

AN - SCOPUS:14944371769

VL - 36

SP - 552

EP - 579

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 2

ER -