On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity

International audienceLet Ω be an open connected subset of R^3 and let Θ be an immersion from Ω into R^3. It is established that the set formed by all rigid displacements of the open set Θ(Ω) is a submanifold of dimension 6 and of class C^∞ of the space H^1(Ω). It is also shown that the infinitesimal rigid displacements of the same set Θ(Ω) span the tangent space at the origin to this submanifold