An optimal Hardy–Morrey inequality

An Optimal Double Inequality for Means

For p ∈ R, the generalized logarithmic mean Lp a, b , arithmetic mean A a, b and geometric mean G a, b of two positive numbers a and b are defined by Lp a, b a, a b; Lp a, b a 1 − b 1 / p 1 a − b , p / 0, p / − 1, a/ b; Lp a, b 1/e b/a 1/ b−a , p 0, a/ b; Lp a, b b − a / ln b − lna , p −1, a/ b; A a, b a b /2 and G a, b √ ab, respectively. In this paper, we give an answer to the open problem: f...

Minimizing Neumann Fundamental Tones of Triangles: an Optimal Poincaré Inequality

The first nonzero eigenvalue of the Neumann Laplacian is shown to be minimal for the degenerate acute isosceles triangle, among all triangles of given diameter. Hence an optimal Poincaré inequality for triangles is derived. The proof relies on symmetry of the Neumann fundamental mode for isosceles triangles with aperture less than π/3. Antisymmetry is proved for apertures greater than π/3.

Towards an Optimal Synthetic Index for Measuring Gender Inequality

Gender equality is a key aspect of human rights in order to achieve sustainability and development focused on people. Bearing in mind how important equality has become in decision making, indicators including the gender approach are useful for quantifying the differences between the two genders and how they have evolved over time. Taking gender into account brings a diverse and complex reality ...

An Optimal Double Inequality between Seiffert and Geometric Means

An Optimal Shape Design Problem for a Hyperbolic Hemivariational Inequality

In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.