We study relations between the k-Hessian energy, and the fractional Sobolev energy , where F k (k = 1, . . . , n) is the k-Hessian operator on ℝ n , and u is a k-convex function vanishing at ∞. We prove that there is a constant C > 0 such that C^(-1) E k [u] ≦ ℰ k [u] ≦ CE k [u], where the lower estimate is obtained under some additional assumptions on u.

Hessian inequalities and the fractional Laplacian

FERRARI, FAUSTO;FRANCHI, BRUNO;
2012

Abstract

We study relations between the k-Hessian energy, and the fractional Sobolev energy , where F k (k = 1, . . . , n) is the k-Hessian operator on ℝ n , and u is a k-convex function vanishing at ∞. We prove that there is a constant C > 0 such that C^(-1) E k [u] ≦ ℰ k [u] ≦ CE k [u], where the lower estimate is obtained under some additional assumptions on u.
2012
F. Ferrari; B. Franchi; I. E. Verbitsky
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/117072
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 9
social impact