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.
Titolo: | On the role of gradient terms in coercive quasilinear differential inequalities on Carnot groups |
Autori: | ALBANESE, GUGLIELMO (Primo) MARI, LUCIANO (Secondo) RIGOLI, MARCO (Ultimo) |
Parole Chiave: | A priori estimates; Carnot groups; Liouville-type theorems; Weak maximum principle; Analysis; Applied Mathematics |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
Data di pubblicazione: | 2015 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.na.2015.06.006 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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