If G is a compact Lie group acting linearly on a Banach space X and f is a G-invariant function on X, we provide some new versions of the so-called Palais’ principle of symmetric criticality for f : X → R, in the framework of non-smooth critical point theory. We apply the results to a class of quasi-linear PDEs associated with invariant functionals which are merely lower semi-continuous and thus could not be treated by previous non-smooth versions of the principle in the literature.
Squassina, M., On Palais' principle for nonsmooth functionals, <<NONLINEAR ANALYSIS>>, 2011; 74 (N/A): 3786-3804 [http://hdl.handle.net/10807/89763]
On Palais' principle for nonsmooth functionals
Squassina, MarcoPrimo
2011
Abstract
If G is a compact Lie group acting linearly on a Banach space X and f is a G-invariant function on X, we provide some new versions of the so-called Palais’ principle of symmetric criticality for f : X → R, in the framework of non-smooth critical point theory. We apply the results to a class of quasi-linear PDEs associated with invariant functionals which are merely lower semi-continuous and thus could not be treated by previous non-smooth versions of the principle in the literature.File in questo prodotto:
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