On a nonlocal elliptic problem arising in the confinement of a plasma in a current carrying stellarator.

This paper deals with a nonlocal free boundary problem arising in the study of the dynamics of the confinement of a plasma in a Stellarator device. The free boundary represents the separation between the plasma and vacuum regions, and the nonlocal term involves the notions of relative rearrangement and monotone rearrangement. We establish some new properties on the decreasing rearrangement that can be used to prove the convergence of the approximate problem, and then prove the existence of solutions by Galerkin method. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]