Characterizations of differentiability for h-convex functions in stratified groups

• Valentino Magnani ^[1] ; Matteo Scienza ^[1]
  1. [1] Dipartimento di Matematica, Pisa, Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 3, 2014, págs. 675-697
• Idioma: inglés
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• Resumen

  • Using the notion of h-subdifferential, we characterize both first and second order differentiability of h-convex functions in stratified groups. Besides some new results involving the h-subdifferential of h-convex functions, we show that at all h-differentiability points of an h-convex function, the existence of a second order expansion coincides with a suitable differentiability of its horizontal gradient.