In the sub-Riemannian setting of Carnot groups, this work investigates a priori estimates and Liouville type theorems for solutions of coercive, quasilinear differential inequalities of the type (Formula presented.). Prototype examples of (Formula presented.) are the (subelliptic) p-Laplacian and the mean curvature operator. The main novelty of the present paper is that we allow a dependence on the gradient l(t) that can vanish both as t→0+ and as t→+∞. Our results improve on the recent literature and, by means of suitable counterexamples, we show that the range of parameters in the main theorems are sharp.

On the role of gradient terms in coercive quasilinear differential inequalities on Carnot groups / G. Albanese, L. Mari, M. Rigoli. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 126(2015), pp. 234-261. [10.1016/j.na.2015.06.006]

On the role of gradient terms in coercive quasilinear differential inequalities on Carnot groups

G. Albanese
Primo
;
L. Mari
Secondo
;
M. Rigoli
Ultimo
2015

Abstract

In the sub-Riemannian setting of Carnot groups, this work investigates a priori estimates and Liouville type theorems for solutions of coercive, quasilinear differential inequalities of the type (Formula presented.). Prototype examples of (Formula presented.) are the (subelliptic) p-Laplacian and the mean curvature operator. The main novelty of the present paper is that we allow a dependence on the gradient l(t) that can vanish both as t→0+ and as t→+∞. Our results improve on the recent literature and, by means of suitable counterexamples, we show that the range of parameters in the main theorems are sharp.
A priori estimates; Carnot groups; Liouville-type theorems; Weak maximum principle; Analysis; Applied Mathematics
Settore MAT/03 - Geometria
Article (author)
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0362546X15002011-main.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 794.27 kB
Formato Adobe PDF
794.27 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

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: http://hdl.handle.net/2434/473740
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 1
social impact