Singularities of the quad curl problem

Serge Nicaise (1, 2)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 UPHF - Université Polytechnique Hauts-de-France

We consider the quad curl problem in smooth and non smooth domains of the space. We first give an augmented variational formulation equivalent to the one from [29] if the datum is divergence free. We describe the singularities of the variational space that correspond to the ones of the Maxwell system with perfectly conducting boundary conditions. The edge and corner singularities of the solution of the corresponding boundary value problem with smooth data are also characterized. We finally obtain some regularity results of the variational solution.

Mots clés: Fourth order problem; Maxwell system; Singularities

Domaines: Equations aux dérivées partielles [math.AP]

Serge Nicaise. Singularities of the quad curl problem. Journal of Differential Equations, 2018, 264 (8), pp.5025-5069. ⟨10.1016/j.jde.2017.12.032⟩. ⟨hal-01324641v2⟩