In this paper we give conditions on the positive function phi(2) under which every bounded solution sigma of the elliptic equation V.(phi(2)delsigma) = 0 in R-n must be constant. The case when phi(2) only depends on one or two variables is discussed at length. Moreover the asymptotic behavior of possibly unbounded solutions is characterized improving in such a way a Liouville theorem due to Berestycki, Caffarelli and Nirenberg. (C) 2004 Elsevier SAS. All rights reserved.
New Liouville theorems for linear second order degenerate elliptic equations in divergence form / Moschini, Luisa. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 22:1(2005), pp. 11-23. [10.1016/j.anihpc.2004.03.001]
New Liouville theorems for linear second order degenerate elliptic equations in divergence form
MOSCHINI, Luisa
2005
Abstract
In this paper we give conditions on the positive function phi(2) under which every bounded solution sigma of the elliptic equation V.(phi(2)delsigma) = 0 in R-n must be constant. The case when phi(2) only depends on one or two variables is discussed at length. Moreover the asymptotic behavior of possibly unbounded solutions is characterized improving in such a way a Liouville theorem due to Berestycki, Caffarelli and Nirenberg. (C) 2004 Elsevier SAS. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
