A class of stationary nonlinear Maxwell systems

Abstract

We study a new class of electromagnetostatic problems in the variational framework of the subspace of $W^{1,p}(\Omega)^3$ of vector functions with zero divergence and zero normal trace, for $p>6/5$, in smooth, bounded and simply connected domains $\Omega$ of $\mathbb R^3$. We prove a Poincaré-Friedrichs type inequality and we obtain the existence of steady-state solutions for an electromagnetic induction heating problem and for a quasi-variational inequality modelling a critical state generalized problem for type-II superconductors.