The principle of symmetric criticality for non-differentiable mappings

Jun Kobayashi, Mitsuharu Otani

    Research output: Contribution to journalArticle

    15 Citations (Scopus)

    Abstract

    Let X be a Banach space on which a symmetry group G linearly acts and let J be a G-invariant functional defined on X. In 1979, R. Palais (Comm. Math. Phys. 69 (1979) 19) gave some sufficient conditions to guarantee the so-called "Principle of Symmetric Criticality": every critical point of J restricted on the subspace of G-symmetric points becomes also a critical point of J on the whole space X. This principle is generalized to the case where J is not differentiable within the setting which does not require the full variational structure under the hypothesis that the action of G is isometry or G is compact.

    Original languageEnglish
    Pages (from-to)428-449
    Number of pages22
    JournalJournal of Functional Analysis
    Volume214
    Issue number2
    DOIs
    Publication statusPublished - 2004 Sep 15

    Fingerprint

    Criticality
    Critical point
    Symmetry Group
    Isometry
    Differentiable
    Linearly
    Subspace
    Banach space
    Invariant
    Sufficient Conditions

    Keywords

    • Elliptic variational inequality
    • Group action
    • Non-smooth functional
    • Subdifferential operator
    • Symmetric criticality

    ASJC Scopus subject areas

    • Analysis

    Cite this

    The principle of symmetric criticality for non-differentiable mappings. / Kobayashi, Jun; Otani, Mitsuharu.

    In: Journal of Functional Analysis, Vol. 214, No. 2, 15.09.2004, p. 428-449.

    Research output: Contribution to journalArticle

    @article{5f78bc03f07649e78d863fa020375495,
    title = "The principle of symmetric criticality for non-differentiable mappings",
    abstract = "Let X be a Banach space on which a symmetry group G linearly acts and let J be a G-invariant functional defined on X. In 1979, R. Palais (Comm. Math. Phys. 69 (1979) 19) gave some sufficient conditions to guarantee the so-called {"}Principle of Symmetric Criticality{"}: every critical point of J restricted on the subspace of G-symmetric points becomes also a critical point of J on the whole space X. This principle is generalized to the case where J is not differentiable within the setting which does not require the full variational structure under the hypothesis that the action of G is isometry or G is compact.",
    keywords = "Elliptic variational inequality, Group action, Non-smooth functional, Subdifferential operator, Symmetric criticality",
    author = "Jun Kobayashi and Mitsuharu Otani",
    year = "2004",
    month = "9",
    day = "15",
    doi = "10.1016/j.jfa.2004.04.006",
    language = "English",
    volume = "214",
    pages = "428--449",
    journal = "Journal of Functional Analysis",
    issn = "0022-1236",
    publisher = "Academic Press Inc.",
    number = "2",

    }

    TY - JOUR

    T1 - The principle of symmetric criticality for non-differentiable mappings

    AU - Kobayashi, Jun

    AU - Otani, Mitsuharu

    PY - 2004/9/15

    Y1 - 2004/9/15

    N2 - Let X be a Banach space on which a symmetry group G linearly acts and let J be a G-invariant functional defined on X. In 1979, R. Palais (Comm. Math. Phys. 69 (1979) 19) gave some sufficient conditions to guarantee the so-called "Principle of Symmetric Criticality": every critical point of J restricted on the subspace of G-symmetric points becomes also a critical point of J on the whole space X. This principle is generalized to the case where J is not differentiable within the setting which does not require the full variational structure under the hypothesis that the action of G is isometry or G is compact.

    AB - Let X be a Banach space on which a symmetry group G linearly acts and let J be a G-invariant functional defined on X. In 1979, R. Palais (Comm. Math. Phys. 69 (1979) 19) gave some sufficient conditions to guarantee the so-called "Principle of Symmetric Criticality": every critical point of J restricted on the subspace of G-symmetric points becomes also a critical point of J on the whole space X. This principle is generalized to the case where J is not differentiable within the setting which does not require the full variational structure under the hypothesis that the action of G is isometry or G is compact.

    KW - Elliptic variational inequality

    KW - Group action

    KW - Non-smooth functional

    KW - Subdifferential operator

    KW - Symmetric criticality

    UR - http://www.scopus.com/inward/record.url?scp=4344599726&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=4344599726&partnerID=8YFLogxK

    U2 - 10.1016/j.jfa.2004.04.006

    DO - 10.1016/j.jfa.2004.04.006

    M3 - Article

    VL - 214

    SP - 428

    EP - 449

    JO - Journal of Functional Analysis

    JF - Journal of Functional Analysis

    SN - 0022-1236

    IS - 2

    ER -