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# On a free-boundary problem modeling the action of a limiter on a plasma

• In this paper we prove the existence of weak solutions for a 2D free–boundary problems arising in the magnetic confinement of a plasma in a Stellarator device which includes the action of a limiter. The model can be expressed as an inverse thin obstacle problem in which the limiter plays the role of a thin obstacle for the plasma. The inverse nature of the problem comes from the fact that the associated Grad–Shafranov equation involves some unknown nonlinear terms which must be determined by the current–carrying Stellarator condition.
Mathematics Subject Classification: Primary: 35J85; Secondary: 35R30.

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