Calculus of Variations and Geometric Measure Theory

D. Bartolucci - Y. Hu - A. Jevnikar - W. Yang

Generic properties of free boundary problems in plasma physics

created by jevnikar on 08 Jun 2021
modified on 13 Nov 2021


Accepted Paper

Inserted: 8 jun 2021
Last Updated: 13 nov 2021

Journal: Nonlinearity
Year: 2021


We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape of the branch of solutions resembles the monotone one of the model case of the two-dimensional disk, or it is a continuous simple curve without bifurcation points which ends up at a point where the boundary density vanishes. On the other hand, we deduce a general criterion ensuring the existence of a free boundary in the interior of the domain. Application to a classic nonlinear eigenvalue problem is also discussed.

Keywords: free boundary problem, bifurcation analysis, plasma physics, generic properties