A closed subset M of a Banach space E is epi-Lipschitzian, i.e., can be represented locally as the epigraph of a Lipschitz function, if and only if it is the level set of some locally Lipschitz function f : E β R, for which Clarke's generalized gradient does not contain 0 at points in the boundary o
Smooth representations of epi-Lipschitzian subsets of Rn
β Scribed by Bernard Cornet; Marc-Olivier Czarnecki
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 177 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0362-546X
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## Abstract We give an intrinsic characterization of the restrictions of Sobolev $W^{k}\_{p}$ (β^__n__^ ), TriebelβLizorkin $F^{s}\_{pq}$(β^__n__^ ) and Besov $B^{s}\_{pq}$(β^__n__^ ) spaces to regular subsets of β^__n__^ via sharp maximal functions and local approximations. (Β© 2006 WILEYβVCH Verl
The paper is devoted to the study of the so-called compactly epi-Lipschitzian sets. These sets are needed for many aspects of generalized di erentiation, particulary for necessary optimality conditions, stability of mathematical programming problems and calculus rules for subdi erentials and normal