Search results for "Tangent measure"

Dimensional reduction for energies with linear growth involving the bending moment

2008

A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.

Tangent measures and densities

1995

Tangent Measures, Densities, and Singular Integrals

1995

We introduce tangent measures in the sense of David Preiss. We discuss their applications to the density and rectifiability properties of general Borel measures in ℝ n as well as to the behaviour of certain singular integrals with respect to such measures.

Rectifiability, weak linear approximation and tangent measures

1995