We study the asymptotic behavior as n ->infinity of a sequence of functions u(n) satisfying the Emden equation Delta u(n) = e(un) in a bounded domain Omega subset of R-N, with N >= 2. By assuming a suitable uniform bound and an additional monotonicity property, we prove that the *-weak limit in the sense of measures of a subsequence of e(un) is either a function of L-1(Omega), or a purely singular measure concentrated on an (N - 2)-rectifiable set.
Uniform estimates and blow-up analysis for the Emden exponential equation in any dimension / Orsina, Luigi; Bartolucci, Daniele; Leoni, Fabiana. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 9:2(2007), pp. 163-182. [10.1142/s0219199707002411]
Uniform estimates and blow-up analysis for the Emden exponential equation in any dimension
ORSINA, Luigi;BARTOLUCCI, DANIELE;LEONI, Fabiana
2007
Abstract
We study the asymptotic behavior as n ->infinity of a sequence of functions u(n) satisfying the Emden equation Delta u(n) = e(un) in a bounded domain Omega subset of R-N, with N >= 2. By assuming a suitable uniform bound and an additional monotonicity property, we prove that the *-weak limit in the sense of measures of a subsequence of e(un) is either a function of L-1(Omega), or a purely singular measure concentrated on an (N - 2)-rectifiable set.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
