Characterization of the kernel of the operator CURL CURL

Abstract

In a simply-connected domain Ω in R 3 , the kernel of the operator CURL CURL acting on symmetric matrix fields from L s 2 ( Ω ) to H s −2 ( 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 L s 2 ( Ω ) . To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).