New Approximations of the Total Variation and Filters in Image Processing
New Approximations of the Total Variation and Filters in Image Processing
ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY
We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the "primary" unknown, instead of the displacement itself as is customary. This approach leads to a well-posed minimization problem, constrained by a weak form of the St Venant compatibility conditions. Interestingly, it also provides a new proof of Korn's inequality.
Continuity of a Deformation as a Function of its Cauchy-Green Tensor
If the Riemann-Christoffel tensor associated with a field C of class 𝒞2 of positive-definite symmetric matrices of order 3 vanishes in a simply connected open subset Ω⊂ℝ3, then this field is the Cauchy-Green tensor field associated with a deformation Θ of class 𝒞3 of the set Ω, and Θ is uniquely determined up to isometries of ℝ3. Let denote the equivalence class formed by all such deformations, and let denote the mapping defined in this fashion. We establish here that the mapping ℱ is continuous, for certain natural metrizable topologies.