# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Local differentiability of distance functions. (English) Zbl 0960.49018
Let $C$ be a closed subset of a Hilbert space, and let $x$ be a prescribed point in the boundary of $C$. The authors discuss the continuous differentiability of the distance function $\text{dist}\left[·;C\right]$ outside of $C$ on some neighborhood of $x$. This paper is an important complement to a previous work by F. H. Clarke, R. J. Stern and P. R. Wolenski [J. Convex Anal. 2, No. 1-2, 117-144 (1995; Zbl 0881.49008)].

##### MSC:
 49J52 Nonsmooth analysis (other weak concepts of optimality) 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds 90C30 Nonlinear programming 58C06 Set-valued and function-space valued mappings on manifolds