Weak vector and scalar potentials. Applications to Poincaré's theorem and Korn's inequality in Sobolev spaces with negative exponents.

Chérif Amrouche 1 Philippe G. Ciarlet 2 Patrick Ciarlet 3
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper, we present several results concerning vector potentials and scalar potentials with data in Sobolev spaces with negative exponents, in a not necessarily simply-connected, three-dimensional domain. We then apply these results to Poincaré's theorem and to Korn's inequality.
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Chérif Amrouche, Philippe G. Ciarlet, Patrick Ciarlet. Weak vector and scalar potentials. Applications to Poincaré's theorem and Korn's inequality in Sobolev spaces with negative exponents.. Analysis and Applications, World Scientific Publishing, 2010, 8 (1), pp.1-17. ⟨10.1142/s0219530510001497⟩. ⟨hal-00444185⟩

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