The coarea inequality

The Coarea Formula for Sobolev Mappings

We extend Federer’s coarea formula to mappings f belonging to the Sobolev class W (R;R), 1 ≤ m < n, p > m, and more generally, to mappings with gradient in the Lorentz space L(R). This is accomplished by showing that the graph of f in R is a Hausdorff n-rectifiable set.

The Brunn-Minkowski-Type Inequality

On the metric triangle inequality

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

A coarea-type formula for the relaxation of a generalized elastica functional

We consider the generalized elastica functional defined on L1(R2) as F(u) =  ∫ R2 |∇u|(α +β |div ∇u |∇u| |p)dx, if u ∈ C2(R2), +∞ else, where p > 1, α > 0, β ≥ 0. We study the L1-lower semicontinuous envelope F of F and we prove that, for any u ∈ BV(R2), F(u) can be represented by a coarea-type formula involving suitable collections of W2,p curves that cover the essential boundaries of the le...

Investigating The Effect of Education Inequality on Inequality of Income Distribution in Iran’s Provinces

Introduction: Inequality of income distribution is one of the socio-economic issues of developing countries, including Iran. One of the proposed solutions to deal with this phenomenon is to reduce educational inequality. The purpose of this study is to investigate the effect of educational inequality on income inequality in the provinces of the country during the years 1380 to 1394. Method: In...