Preprint 51/2002

On a nonlinear elliptic equation arising in a free boundary problem

Guofang Wang and Dong Ye

Contact the author: Please use for correspondence this email.
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
Bibtex
MSC-Numbers: 35J60
Keywords and phrases: free boundary problem, liouville equation
Download full preprint: PDF (251 kB), PS ziped (226 kB)

Abstract:
Let formula22 and formula24. In this paper, we first classify all non-constant solutions of
displaymath20
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.

03.07.2017, 01:40