New universal estimates for free boundary problems arising in plasma physics

Abstract

For Ω ⊂ R 2 a smooth and bounded domain, we derive new universal estimates for free boundary problems on Ω arising in plasma physics. More precisely, the goal of this paper is twofold: first, we show an explicit bound for the L ∞ -norm of positive solutions; second, we obtain explicit estimates for the positivity threshold of the boundary values. This yields also explicit conditions which guarantee that there is no free boundary inside Ω. At least to our knowledge, these are the first explicit estimates of this sort in the superlinear case.