UNIFORM ESTIMATES AND BLOW-UP ANALYSIS FOR THE EMDEN EXPONENTIAL EQUATION IN ANY DIMENSION-Reference-Cited by-同舟云学术

UNIFORM ESTIMATES AND BLOW-UP ANALYSIS FOR THE EMDEN EXPONENTIAL EQUATION IN ANY DIMENSION

Published:2007-04 Issue:02 Volume:09 Page:163-182
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

BARTOLUCCI DANIELE¹,LEONI FABIANA²,ORSINA LUIGI²

Affiliation:

1. Dipartimento di Matematica , Università degli Studi "Roma Tre", L.go S. Leonardo Murialdo 1, I–00146 Roma, Italy

2. Dipartimento di Matematica, Università degli Studi di Roma "La Sapienza" P.le Aldo Moro 2, I–00185 Roma, Italy

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199707002411

Reference7 articles.

1. Semilinear equations with exponential nonlinearity and measure data

2. Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)euin two dimensions

3. Elliptic Partial Differential Equations of Second Order

4. On Morrey spaces of measures: basic properties and potential estimates

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