Stable solutions to Landau-Lifshitz-Maxwell equations Jian Zhai 35B3535J6535K5535Q60Landau-Lifshitz-Maxwell equationsstabilitydemagnetizing field We prove the existence of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with the Neumann boundary condition for large anisotropies and small domains, where the domains are non-simply connected and rotationally invariant around an axis. The Landau-Lifshitz-Maxwell equations describe ferromagnets including the demagnetizing field effect. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2591 10.1512/iumj.2005.54.2591 en Indiana Univ. Math. J. 54 (2005) 1635 - 1660 state-of-the-art mathematics http://iumj.org/access/