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.
F. Ferrari, B. Franchi, I. E. Verbitsky (2012). Hessian inequalities and the fractional Laplacian. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 667, 133-148 [10.1515/CRELLE.2011.116].
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.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.
