Approximate smoothings of locally Lipschitz functionals

Ćwiszewski, Aleksander ; Kryszewski, Wojciech

Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 289-320 / Harvested from Biblioteca Digitale Italiana di Matematica

Abstract

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 $\mathbb{R}^{N}$, 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.

Résumé

L'articolo tratta il problema dell'approssimazione di funzionali localmente Lipschitziani. Viene proposto un concetto di approssimazione che si basa sull'idea dell'approssimazione in grafico del gradiente generalizzato. Si prova l'esistenza di tali approssimazioni per funzionali localmente Lipschitziani definiti in domini aperti di $\mathbb{R}^{N}$. Infine, si presenta un procedimento di approssimazione normale regolare di insiemi regolari (introdotti in [13]).

Détail

Publié le : 2002-06-01

MR 1911193 | Zbl 1177.49028

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