We prove a Liouville type theorem for arbitrarily growing positive viscosity supersolutions of fully nonlinear uniformly elliptic equations in halfspaces. Precisely, let M-lambda.Lambda(-) be the Pucci's inf-operator with ellipticity constants Lambda >= lambda > 0. We prove that the inequality M-lambda.Lambda(-)(D(2)u) + u(P) <= 0 does not have any positive viscosity solution in a halfspace provided that -1 <= p <= Lambda/lambda n+1/Lambda/lambda n-1, 2 whereas positive solutions do exist if either p < -1 or p > Lambda/lambda(n-1)+2/Lambda/lambda(n-1). The proof relies on the construction of explicit subsolutions of the homogeneous equation M-lambda.Lambda(-) (D(2)u) = 0 and on a nonlinear version in a halfspace of the classical Hadamard three-circles theorem for entire superharmonic functions. (C) 2012 Elsevier Masson SAS. All rights reserved.

Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces / Leoni, Fabiana. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 98:5(2012), pp. 574-590. [10.1016/j.matpur.2012.05.003]

Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces

LEONI, Fabiana
2012

Abstract

We prove a Liouville type theorem for arbitrarily growing positive viscosity supersolutions of fully nonlinear uniformly elliptic equations in halfspaces. Precisely, let M-lambda.Lambda(-) be the Pucci's inf-operator with ellipticity constants Lambda >= lambda > 0. We prove that the inequality M-lambda.Lambda(-)(D(2)u) + u(P) <= 0 does not have any positive viscosity solution in a halfspace provided that -1 <= p <= Lambda/lambda n+1/Lambda/lambda n-1, 2 whereas positive solutions do exist if either p < -1 or p > Lambda/lambda(n-1)+2/Lambda/lambda(n-1). The proof relies on the construction of explicit subsolutions of the homogeneous equation M-lambda.Lambda(-) (D(2)u) = 0 and on a nonlinear version in a halfspace of the classical Hadamard three-circles theorem for entire superharmonic functions. (C) 2012 Elsevier Masson SAS. All rights reserved.
2012
homogeneous subsolutions; critical exponents; viscosity supersolutions; fully nonlinear uniformly elliptic equations in halfspaces
01 Pubblicazione su rivista::01a Articolo in rivista
Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces / Leoni, Fabiana. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 98:5(2012), pp. 574-590. [10.1016/j.matpur.2012.05.003]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

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/11573/498223
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact