The principle of symmetric criticality for non-differentiable mappings

Jun Kobayashi, Mitsuharu Otani

    Research output: Contribution to journalArticle

    19 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

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

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