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.
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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, Wiley, 2001, 24 (1), pp.31-48. ⟨10.1002/1099-1476(20010110)24:1(31::aid-mma193)3.0.co;2-x⟩. ⟨hal-00878224⟩

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