1.1. Introduction. Set up by Hardy & Littlewood, a theory of rearrangements was popularized
by the well-known book HLP]. Rearrangements of functions are frequently used in real and …

We establish an existence result for the three‐dimensional MHD equations (∇ *\bf B) *\bf B=
∇ p ∇ ⋅\bf B= 0\bf B ⋅ n ∂ T= 0 with p≠ const in tori T without symmetry. More precisely …

A new variational approach is proposed for a class of semilinear elliptic eigenvalue
problems involving many eigenvalue parameters. These problems arise, for instance, in the …

The purpose of this paper is to show how convexity properties lead to sharp estimates for
geometric quantities related to level curves of solutions to some classical partial differential …

Setting F (ti)= A we are led (formally) to the free boundary problems mentioned previously. In
[L-S2] we establish existence of solutions to Problems I and II which have convex level lines …

In this paper we generalize an equation studied by Mossino and Temam in [7], to the fully
nonlinear case. This equation arises in plasma physics as an approximation to Grad …

A computational method is proposed for solving magnetohydrodynamical equilibrium
problems with prescribed flux and mass within the magnetic surfaces that foliate the plasma …

1.1. Problem. In Rm, m 2 2, let an annular domain R of the form R= D,+,\CI (Do) be given,
where n> 1 and Do, D,+, are fixed, bounded, simply-connected, nested C1-domains. Given …

[Ck] and [Cr]. Although this method of computing free boundaries has been in use for
approximately 75 years, there are very fi: w cases where convergence proofs have been …

We consider a class of degenerate elliptic fully nonlinear equations with applications to Grad
equations:\begin {align}\begin {cases}| Du|^\gamma\mathcal {M} _ {\lambda,\Lambda}^+\big …