On a nonlinear elliptic equation arising in a free boundary problem |
| |
| Authors: | Guofang Wang Dong Ye |
| |
| Institution: | (1) Max-Planck-Institute for Mathematics, Inselstr. 22-26, D-04103 Leipzig, Germany (e-mail: gwang@mis.mpg.de), DE;(2) Département de Mathématiques, site Saint-Martin, Université de Cergy-Pontoise, BP222, 95302 Cergy-Pontoise cedex, France, FR;(3) C.M.L.A., E.N.S. de Cachan, 61 avenue du Président Wilson, 94235 Cachan cedex, France (e-mail: dong.ye@math.u-cergy.fr), FR |
| |
| Abstract: | Let p
*
=n/(n−2) and n≥3. In this paper, we first classify all non-constant solutions of We then establish a sup + inf and a Moser-Trudinger type inequalities for the equation −Δu=u
+
p*
. Our results illustrate that this equation is much closer to the Liouville problem −Δu=e
u
in dimension two than the usual critical exponent equation, namely is.
Received: 11 March 2002; in final form: 8 July 2002 /
Published online: 16 May 2003 |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
