ASYMPTOTIC BEHAVIOR OF BLOWUP SOLUTIONS FOR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA

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 pro. le 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.