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Global Compactness Properties of Semilinear Elliptic Equations with Critical Exponential Growth

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
175
Issue
1
Identifiers
DOI: 10.1006/jfan.2000.3602
Disciplines
  • Mathematics

Abstract

Abstract Sequences of positive solutions to semilinear elliptic equations of critical exponential growth in the plane either are precompact in the Sobolev H 1-topology or concentrate at isolated points of the domain. For energies allowing at most single-point blow-up, we establish a universal blow-up pattern near the concentration point and uniquely characterize the blow-up energy in terms of a geometric limiting problem.

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