Convexified Gauss curvature flow of sets: A stochastic approximation

Hitoshi Ishii, Toshio Mikami

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)552-579
    Number of pages28
    JournalSIAM Journal on Mathematical Analysis
    Volume36
    Issue number2
    DOIs
    Publication statusPublished - 2005

    Fingerprint

    Curvature Flow
    Gauss Curvature
    Stochastic Approximation
    Bounded Set
    Open set
    Discrete Approximation
    Viscosity Solutions
    External Field
    Weak Solution
    Viscosity
    Motion

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics
    • Numerical Analysis

    Cite this

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

    In: SIAM Journal on Mathematical Analysis, Vol. 36, No. 2, 2005, p. 552-579.

    Research output: Contribution to journalArticle

    Ishii, Hitoshi ; Mikami, Toshio. / Convexified Gauss curvature flow of sets : A stochastic approximation. In: SIAM Journal on Mathematical Analysis. 2005 ; Vol. 36, No. 2. pp. 552-579.
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