Motion of a Graph by R-Curvature

Hitoshi Ishii, Toshio Mikami

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We show the existence of weak solutions to the partial differential equation which describes the motion by R-curvature in Rd, 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.

    Original languageEnglish
    Pages (from-to)1-23
    Number of pages23
    JournalArchive for Rational Mechanics and Analysis
    Volume171
    Issue number1
    DOIs
    Publication statusPublished - 2004 Jan

    Fingerprint

    Viscosity Solutions
    Partial differential equations
    Weak Solution
    Partial differential equation
    Infinite Particle System
    Curvature
    Viscosity
    Motion
    Existence of Weak Solutions
    Continuum Limit
    Graph in graph theory
    Uniqueness
    Class

    ASJC Scopus subject areas

    • Mechanics of Materials
    • Computational Mechanics
    • Mathematics(all)
    • Mathematics (miscellaneous)

    Cite this

    Motion of a Graph by R-Curvature. / Ishii, Hitoshi; Mikami, Toshio.

    In: Archive for Rational Mechanics and Analysis, Vol. 171, No. 1, 01.2004, p. 1-23.

    Research output: Contribution to journalArticle

    Ishii, Hitoshi ; Mikami, Toshio. / Motion of a Graph by R-Curvature. In: Archive for Rational Mechanics and Analysis. 2004 ; Vol. 171, No. 1. pp. 1-23.
    @article{b45ee76aa27e4fe5acf40737ad1cf1ad,
    title = "Motion of a Graph by R-Curvature",
    abstract = "We show the existence of weak solutions to the partial differential equation which describes the motion by R-curvature in Rd, 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.",
    author = "Hitoshi Ishii and Toshio Mikami",
    year = "2004",
    month = "1",
    doi = "10.1007/s00205-003-0294-1",
    language = "English",
    volume = "171",
    pages = "1--23",
    journal = "Archive for Rational Mechanics and Analysis",
    issn = "0003-9527",
    publisher = "Springer New York",
    number = "1",

    }

    TY - JOUR

    T1 - Motion of a Graph by R-Curvature

    AU - Ishii, Hitoshi

    AU - Mikami, Toshio

    PY - 2004/1

    Y1 - 2004/1

    N2 - We show the existence of weak solutions to the partial differential equation which describes the motion by R-curvature in Rd, 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.

    AB - We show the existence of weak solutions to the partial differential equation which describes the motion by R-curvature in Rd, 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.

    UR - http://www.scopus.com/inward/record.url?scp=0742306187&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0742306187&partnerID=8YFLogxK

    U2 - 10.1007/s00205-003-0294-1

    DO - 10.1007/s00205-003-0294-1

    M3 - Article

    AN - SCOPUS:0742306187

    VL - 171

    SP - 1

    EP - 23

    JO - Archive for Rational Mechanics and Analysis

    JF - Archive for Rational Mechanics and Analysis

    SN - 0003-9527

    IS - 1

    ER -