Principle of symmetric criticality and evolution equations
Goro Akagi - Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan (email)
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  gave some sufficient conditions to guarantee the so-called "Principle of Symmetric Criticality": every critical point of J restricted on the subspace of symmetric points becomes also a critical point of J on the whole space X. In , this principle was generalized to the case where J is non-smooth and the setting does not require the full variational structure when G is compact or isometric.
Keywords: symmetric criticality, group action, evolution equations, subdifferential, p-Laplacian, unbounded domain.
Received: September 2002; Revised: March 2003; Published: July 2003.