Iwona Skrzypczak

On Certain New Method to Construct Weighted Hardy-Type Inequalities and Its Application to the Sharp Hardy-Poincaré Inequalities

We apply the recent method of Drabek and the authors in order to construct the Hardy–Poincare–type inequalities

Nonexistence results for differential inequalities involving

\begin{aligned} \bar{C}_{\gamma ,n,p,r}\int _{\mathbb {R}^{n}}\ |\xi |^p \left( 1+r|x|^{\frac{p}{p-1}}\right) \left( 1+|x|^{\frac{p}{p-1}}\right) ^{\gamma (p-1)-p}\, dx\\ \le \int _{\mathbb {R}^{n}}|\nabla \xi |^p\left( 1+|x|^{\frac{p}{p-1}}\right) ^{\gamma (p-1)}\, dx.\end{aligned}

-Laplacian

Some of the derived inequalities are proven to hold with the best constants.