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Displaying similar documents to “An intermediate existence theory in the calculus of variations”

Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably...

Approximate smoothings of locally Lipschitz functionals

Aleksander Ćwiszewski, Wojciech Kryszewski (2002)

Bollettino dell'Unione Matematica Italiana

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The paper deals with approximation of locally Lipschitz functionals. A concept of approximation, based on the idea of graph approximation of the generalized gradient, is discussed and the existence of such approximations for locally Lipschitz functionals, defined on open domains in R N , is proved. Subsequently, the procedure of a smooth normal approximation of the class of regular sets (containing e.g. convex and/or epi-Lipschitz sets) is presented.