Abstract
The purpose of this lecture is to survey some recent results concerning a free boundary value problem which describes the equilibrium of a plasma confined in a Tokomak machine. Section 1 contains the derivation of the equations and the general formulation of the problem. Section 2 gives the variational formulation of the problem and a statement of the main results for a particular problem which is however significant. Section 3 contains some indications on the results obtained in other cases, and finally Section 4 is devoted to open problems : among these let us already mention - a singular perturbation problem - two problems of bifurcation and existence of multiple solutions in non standard situations : one of these is related to the case where the perturbation is not smooth (and in some instances may not be small).
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