A method of super and subsolutions applied to the localization of solutions of the plasma axisymmetric equilibrium in a tokamak

This paper deals with a class of free boundary value problems issued from t he physic of confined plasmas. By the use of the maximum principle and of a fixed point technique, analogous to the one of A. Bensoussan and J.-L. Lio ns [1] for quasi-variational inequalities, modelling stock management probl ems, we obtain a localization of the solution in an interval order smaller than the interval order of the initial sub and supersolution data of the su ccessive approximation algorithm. We need here to use an isotone-antitone f ixed point mapping. (C) 2000 Academie des sciences/Editions scientifiques e t medicales Elsevier SAS.