Summary
We discuss some questions relevant to the solution of the interior Dirichlet problem for the (linear, non-self-adjoint) elliptic operator\(L \equiv \partial _{R^2 } + \partial _{Z^2 } - 1/R\partial _R \). As is well known, this problem plays a major role in the magnetofluid dynamic description of the toroidal, axisymmetric plasma in a Tokamak.
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References
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We shall name as «toroid» the 3-dimensional domain generated by rotation of a corresponding domain Ω in the half-plane (R≥0,Z) about theZ-axis. A «nonsingular» toroid is one with Ω at strictly positive distance from theZ-axis.
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Surdo, C.L. Some aspects of the axisymmetric magnetohydrostatic problem. Nuov Cim B 107, 39–46 (1992). https://doi.org/10.1007/BF02726881
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DOI: https://doi.org/10.1007/BF02726881