Funzioni semiconcave, singolarità e pile di sabbia

Cannarsa, Piermarco

Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 549-567.

Riassunto (VO)

La semiconcavità è una nozione che generalizza quella di concavità conservandone la maggior parte delle proprietà ma permettendo di ampliarne le applicazioni. Questa è una rassegna dei punti più salienti della teoria delle funzioni semiconcave, con particolare riguardo allo studio dei loro insiemi singolari. Come applicazione, si discuterà una formula di rappresentazione per la soluzione di un modello dinamico per la materia granulare.

Abstract

Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This is a survey of the main properties of semiconcave functions which emphasizes the study of singularities. An application to a dynamic model for granular matter will be discussed.

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