Hardy and Rellich inequality on lattices

• DOI: 10.1007/s00526-022-02407-0
• Publication Date: 2023-01-11T09:03:35Z
• Authors: Shubham Gupta
• Keywords: Nabla symbol; Constant (computer programming); Lattice (music)

In this paper, we study the asymptotic behaviour of sharp constant in discrete Hardy and Rellich inequality on lattice $\mathbb{Z}^d$ as $d \rightarrow \infty$. process, proved some Hardy-type inequalities for operators $\Delta^m$ $\nabla(\Delta^m)$ non-negative integers $m$ a $d$ dimensional torus. It turns out that grows $d^2$ respectively $ d