If (M, g) is a Riemannian manifold and X a vector field on M, then the Lie derivative LXg of g with respect to X is a symmetric tensor. The authors prove some coercive estimates. These estimates are true on Euclidean space, according to Korn. One of these estimates is that if Ω is an open set with C 1,1 boundary, then there is a constant C> 0 such that for every vector field X, C‖∇X ‖ 2 L 2 (Ω) ≤ ‖X‖2 L 2 (Ω) + ‖LXg ‖ L 2 (Ω). The authors also obtains a better estimate when Ω is assumed to be convex and X vanishes on γ ⊂ Ω provided γ has Hausdorff dimension strictly larger than dim M − 2. Reviewed by Gilles Carro
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