On traces for functional spaces related to Maxwell's equations Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications - Archive ouverte HAL Access content directly
Journal Articles Mathematical Methods in the Applied Sciences Year : 2001

On traces for functional spaces related to Maxwell's equations Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications

Abstract

Hedge decompositions of tangential vector fields defined on piecewise regular manifolds are provided. The first step is the study of L-2 tangential fields and then the attention is focused on some particular Sobolev spaces of order - 1/2. In order to reach this goal, it is required to properly define the first order differential operators and to investigate their properties. When the manifold Gamma is the boundary of a polyhedron Omega, these spaces are important in the analysis of tangential trace mappings for vector fields in H(curl, Omega) on the whole boundary or on a part of it. By means of,these Hedge decompositions, one can then provide a complete characterization of these trace mappings: general extension theorems, from the boundary, or from a part of it, to the inside; definition of suitable dualities and validity of integration by parts formulae. Copyright (C) 2001 John Wiley & Sons, Ltd.

Dates and versions

hal-00878224 , version 1 (04-11-2013)

Identifiers

Cite

Annalisa Buffa, Patrick Ciarlet. On traces for functional spaces related to Maxwell's equations Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications. Mathematical Methods in the Applied Sciences, 2001, 24 (1), pp.31-48. ⟨10.1002/1099-1476(20010110)24:1(31::aid-mma193)3.0.co;2-x⟩. ⟨hal-00878224⟩
256 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More