UNIFORM ESTIMATES AND BLOW-UP ANALYSIS FOR THE EMDEN EXPONENTIAL EQUATION IN ANY DIMENSION
Daniele Bartolucci, Fabiana Leoni, Luigi Orsina · Communications in Contemporary Mathematics · 2007
We study the asymptotic behavior as n → ∞ of a sequence of functions un satisfying the Emden equation -Δ un = e un in a bounded domain Ω ⊂ ℝN, 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 L1(Ω), or a purely singular measure concentrated on an (N - 2)-rectifiable set.