The principle of symmetric criticality for non-differentiable mappings

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• 作者：Kobayashi ; Jun ; Ô ; tani ; Mitsuharu
• 关键词：20C99 ; 49J40 ; 49J52 ; 35J85 ; Symmetric criticality ; Subdifferential operator ; Group action ; Non-smooth functional ; Elliptic variational inequality
• 刊名：Journal of Functional Analysis
• 出版年：2004
• 出版时间：September 15, 2004
• 年：2004
• 卷：214
• 期：2
• 页码：428-449
• 全文大小：316 K

文摘

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.