A geometrical version of Hardy-Rellich type inequalities

Year, pages: 2019, 785 - 800

We obtained a version of Hardy-Rellich type inequality in a domain $Ω\in\mathbb{R}ⁿ$ which involves the distance to the boundary, the diameter and the volume of $Ω$. Weight functions in the inequalities depend on the ``mean-distance" function and on the distance function to the boundary of $Ω$. The proved inequalities connect function to first and second order derivatives.

Nasibullin, R. 2019. A geometrical version of Hardy-Rellich type inequalities. In Mathematica Slovaca, vol. 69, no.4, pp. 785-800. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0268

Nasibullin, R. (2019). A geometrical version of Hardy-Rellich type inequalities. Mathematica Slovaca, 69(4), 785-800. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0268

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava