Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data

TL;DR

This paper analyzes the asymptotic behavior of blowup solutions for a class of elliptic equations with exponential nonlinearity and singular data, providing refined expansions and error estimates near blowup points.

Contribution

It improves previous results by deriving precise asymptotic expansions of solutions near blowup points with sharp error bounds.

Findings

Established detailed asymptotic expansions near blowup points

Provided sharp error estimates for the solution profiles

Extended understanding of solution behavior in geometric and physical contexts

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.