The principle of symmetric criticality for non-differentiable mappings

Jun Kobayashi, Mitsuharu Otani*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    33 Citations (Scopus)


    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
    Issue number2
    Publication statusPublished - 2004 Sept 15


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

    ASJC Scopus subject areas

    • Analysis


    Dive into the research topics of 'The principle of symmetric criticality for non-differentiable mappings'. Together they form a unique fingerprint.

    Cite this