Preprint 51/2002

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 
DOI number (of the published article): 10.1007/s00209-003-0493-3
MSC-Numbers: 35J60
Keywords and phrases: free boundary problem, liouville equation
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Let formula22 and formula24. In this paper, we first classify all non-constant solutions of
We then establish a formula26 and a Moser-Trudinger type inequalities for the equation formula28. Our results illustrate that this equation is much closer to the Liouville problem formula30 in dimension two than the usual critical exponent equation, namely formula32 is.

18.10.2019, 02:11