On a nonlinear elliptic equation arising in a free boundary problem

Guofang Wang, and Dong Ye
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Submission date: 26. Jun. 2002
Pages: 20
published in: Mathematische Zeitschrift, 244 (2003) 3, p. 531-548 
MSC-Numbers: 35J60
Keywords and phrases: free boundary problem, liouville equation
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Abstract:
Let and . In this paper, we first classify all non-constant solutions of

We then establish a and a Moser-Trudinger type inequalities for the equation . Our results illustrate that this equation is much closer to the Liouville problem in dimension two than the usual critical exponent equation, namely is.