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Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

R.P. Agarwal, D. O'Regan, D.R. Sahu (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

General method of regularization. I: Functionals defined on BD space

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis problem.

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