We prove the nonexistence of multi-bubble solutions for several types of problems on smooth-bounded convex domains. Problems we study include the Liouville equation -Delta u = lambda e(u) in Omega, u = 0 on partial derivative Omega in R(2), where lambda > 0 is a parameter, and the almost critical problem -Delta u = u(N+2/N-2 - epsilon), u > 0 in Omega, u = 0 on partial derivative Omega in higher dimensions, where epsilon > 0. (C) 2010 Elsevier Inc. All rights reserved.
Nonexistence of multi-bubble solutions to some elliptic equations on convex domains / Grossi, Massimo; Futoshi, Takahashi. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 259:4(2010), pp. 904-917. [10.1016/j.jfa.2010.03.008]
Nonexistence of multi-bubble solutions to some elliptic equations on convex domains
GROSSI, Massimo;
2010
Abstract
We prove the nonexistence of multi-bubble solutions for several types of problems on smooth-bounded convex domains. Problems we study include the Liouville equation -Delta u = lambda e(u) in Omega, u = 0 on partial derivative Omega in R(2), where lambda > 0 is a parameter, and the almost critical problem -Delta u = u(N+2/N-2 - epsilon), u > 0 in Omega, u = 0 on partial derivative Omega in higher dimensions, where epsilon > 0. (C) 2010 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
