Higher $L^p$ regularity for vector fields that satisfy divergence and rotation constraints in dual Sobolev spaces, and application to some low-frequency Maxwell equations
- Druet, Pierre-Étienne
2010 Mathematics Subject Classification
- 35D10 35J55 35Q60
- Low-frequency Maxwell equations, transmission conditions, regularity theory, Div-Curl inequality, Div-Curl Lemma
We show that Lp vector fields over a Lipschitz domain are integrable to higher exponents if their generalized divergence and rotation can be identified with bounded linear operators acting on standard Sobolev spaces. A Div-Curl Lemma-type argument provides compact embedding results for such vector fields. We investigate the regularity of the solution fields for the low-frequency approximation of the Maxwell equations in time-harmonic regime. We focus on the weak formulation 'in H' of the problem, in a reference geometrical setting allowing for material heterogeneities.
- Discrete Contin. Dyn. Syst., 8 (2015) pp. 479--496.