On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra

Annalisa Buffa (1) , Patrick Ciarlet (2)

1 UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia]
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

The aim of this paper is to study the tangential trace and tangential components of fields which belong to the space H(curl, Omega), when Omega is a polyhedron with Lipschitz continuous boundary. The appropriate functional setting is developed in order to suitably define these traces on the whole boundary and on a part of it (for partially vanishing fields and general ones.) In both cases it is possible to define ad hoc dualities among tangential trace and tangential components. In addition, the validity of two related integration by parts formulae is provided. Copyright (C) 2001 John Wiley & Sons, Ltd.

Domaines: Analyse numérique [math.NA]

Annalisa Buffa, Patrick Ciarlet. On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra. Mathematical Methods in the Applied Sciences, 2001, 24 (1), pp.9-30. ⟨10.1002/1099-1476(20010110)24:1(9::aid-mma191)3.0.co;2-2⟩. ⟨hal-00878223⟩