Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data
Analysis of PDEs
2008-10-30 v1 Mathematical Physics
math.MP
Abstract
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.
Cite
@article{arxiv.0810.5143,
title = {Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data},
author = {Lei Zhang},
journal= {arXiv preprint arXiv:0810.5143},
year = {2008}
}
Comments
21 pages. Communications on contemporary mathematics, in press