A Note on Well-posed Problems |
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Authors: | Jean-No?l Corvellec Roberto Lucchetti |
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Institution: | 1. D??partement de Math??matiques et d??Informatique, Universit?? de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860, Perpignan cedex, France 2. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133, Milano, Italia
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Abstract: | A recent result by Ricceri Ri] states that a ${C^{1,1}_{loc}}$ function ${f : X \to {\mathbb R}}$ , where X is a Hilbert space, attains its minimum on any small closed ball around a point where its derivative does not vanish, and that the unique minimum point belongs to the boundary of the ball. The proof is based on a saddle-point theorem. We show that the result, which we extend to Banach spaces having a norm with modulus of convexity of power type 2, can be obtained by means of a purely variational argument. |
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