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
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U2 - 10.1016/j.jfa.2004.04.006
DO - 10.1016/j.jfa.2004.04.006
M3 - Article
AN - SCOPUS:4344599726
VL - 214
SP - 428
EP - 449
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -