Structural properties of singularities of semiconcave functions

• Paolo Albano ^[1] ; Piermarco Cannarsa ^[1]
  1. [1] Università di Roma "Tor Vergata", Italy
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 28, Nº 4, 1999, págs. 719-740
• Idioma: inglés
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• Resumen

  • A semiconcave function on an open domain of R" is a function that can be locally represented as the sum of a concave function plus a smooth one. The local structure of the singular set (non-differentiability points) of such a function is studied in this paper. A new technique is presented to detect singularities that propagate along Lipschitz arcs and, more generally, along sets of higher dimension.

    This approach is then used to analyze the singular set of the distance function from a closed subset of R^n