BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension

Abstract In this manuscript two BMO estimates are obtained, one for Linear Elasticity and Nonlinear Elasticity. It is first shown that the BMO-seminorm of gradient a vector-valued mapping bounded above by constant times symmetric part its gradient, is, Korn inequality in BMO. The uniqueness equilibrium finite deformation whose principal stresses everywhere nonnegative then considered. when second variation energy, considered as function strain, uniformly positive definite at such an solution, there BMO-neighborhood strain space where no other solutions.