J.-B. Bru and W. de Siqueira Pedra
Remarks on the $\Gamma $-regularization of Non-convex and Non-semi-continuous Functionals on Topological Vector Spaces
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ABSTRACT. We show that the minimization problem of any non--convex and non--lower semi--continuous functional on a compact convex subset of a locally convex real topological vector space can be studied via an associated convex and lower semi--continuous functional $\Gamma \left( h
ight) $. This observation uses the notion of $\Gamma $--regularization as a key ingredient. As an application we obtain, on any locally convex real space, a generalization of the Lanford III--Robinson theorem which has
only been proven for separable real Banach spaces. The latter is a characterization of subdifferentials of convex continuous functionals.