%0 Journal Article
%A ZENG Xian-Zhong
%A XIONG Zhi-Guang
%T The Shape of the Least Energy Solution of Quasilinear Elliptic Equations
%D 2000
%R
%J Journal of Jishou University(Natural Sciences Edition)
%P 58-62
%V 21
%N 1
%X This paper deals wi th the shape of the least energy solut ion of quasilinear el liptic equations involving criticale xponents- v pu = - Div( | Du|p- 2Du) = Q( x ) | u|p*- 2u+ E | u|R - 1u x I 8 ,u| 98= 0,where 8 is a bounded domain in RNwith smooth boundary 98, 0< E< K 1, and Ey 0. Q( x ) I C( 8) , RI [ 1, p*) .The fol lowing conclusions are proved:The least energy solution uE of the equat ions satisfies ( after passing to a subse -quence) :| DuE |p w Q-N- ppm SNpDx 0, as Ey 0, in the sense of measure.| uE |p* w Q-Npm SNpD x0, as Ey 0, in the sense of measure.Where Qm= maxx I 8Q( x ) = Q( x 0) , D x 0 be the Dirac mass at x 0, S is the bes t Sobolev cons tant.
%U https://zkxb.jsu.edu.cn/EN/abstract/article_1175.shtml