Characterization of the kernel of the operator CURL CURL

Philippe G. Ciarlet (1) , Patrick Ciarlet (2) , Giuseppe Geymonat (3) , Françoise Krasucki (3)

1 Department of Mathematics [CUHK]
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
3 LMGC - Laboratoire de Mécanique et Génie Civil

In a simply-connected domain Ω in R3, the kernel of the operator CURLCURL acting on symmetric matrix fields from L2s (Ω) to H−2 s (Ω) coincides with the space of linearized strain tensor fields. For not simply-connected domains, Volterra has characterized this kernel for smooth fields. Here we extend this result for domains with a Lipschitz-continuous boundary for fields in L2s (Ω). To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007). © 2007 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Domaines: Equations aux dérivées partielles [math.AP]

Philippe G. Ciarlet, Patrick Ciarlet, Giuseppe Geymonat, Françoise Krasucki. Characterization of the kernel of the operator CURL CURL. Comptes Rendus. Mathématique, 2007, 344 (série I), pp.305-308. ⟨10.1016/j.crma.2007.01.001⟩. ⟨hal-00583961⟩