A semiconcave function on an open domain of 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 .
Albano P., Cannarsa P. (1999). structural Properties of Singularities of Semiconcave Functions. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 28(4), 719-740.
structural Properties of Singularities of Semiconcave Functions
Albano P.;
1999
Abstract
A semiconcave function on an open domain of 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 .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
