# American Institute of Mathematical Sciences

June  2003, 2(2): 259-275. doi: 10.3934/cpaa.2003.2.259

## Asymptotic shape of a solution for the Plasma problem in higher dimensional spaces

 1 Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

Received  July 2002 Revised  February 2003 Published  March 2003

We consider asymptotic shape of a solution for a semilinear elliptic equation in dimensions 3 or over, by using singular perturbation technique. The equations arise in the Plasma Problem. The solution is obtained as a global minimizer of some energy functional. Precisely energy estimates and uniqueness of a solution for limiting problem gives information about asymptotic shape of a solution.
Citation: Masataka Shibata. Asymptotic shape of a solution for the Plasma problem in higher dimensional spaces. Communications on Pure & Applied Analysis, 2003, 2 (2) : 259-275. doi: 10.3934/cpaa.2003.2.259
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