ON THE UNIQUENESS OF SOLUTIONS OF A NONLINEAR ELLIPTIC PROBLEM ARISING IN THE CONFINEMENT OF A PLASMA IN A STELLARATOR DEVICE

We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the e quation are prescribed in a general class of real functions, The inver se problem arises in the modeling of the magnetic confinement of a pla sma in a Stellarator device. The uniqueness proof relies on an L-infin ity-estimate on the solution of an auxiliary nonlocal problem formulat ed in terms of the relative rearrangement of a datum with respect to t he solution.