The Uniform Korn-poincaré Inequality in Thin Domains

  title={The Uniform Korn-poincar{\'e} Inequality in Thin Domains},
  author={Stefan M{\"u}ller},
We study the Korn-Poincaré inequality: ‖u‖ W1,2(Sh) ≤ Ch‖D(u)‖L2(Sh), in domains S that are shells of small thickness of order h, around an arbitrary smooth and closed hypersurface S in R. By D(u) we denote the symmetric part of the gradient ∇u, and we assume the tangential boundary conditions: u · ~n = 0 on ∂S. We prove that Ch remains uniformly bounded as h → 0, for vector fields u in any family of cones (with angle < π/2, uniform in h) around the orthogonal complement of extensions of… CONTINUE READING