Weighted anisotropic Hardy and Rellich type inequalities for general vector fields

TL;DR

This paper develops weighted anisotropic Hardy and Rellich inequalities with boundary terms for general vector fields, extending classical inequalities to more general and complex settings.

Contribution

It introduces new weighted anisotropic Hardy and Rellich inequalities for general vector fields, including boundary terms, broadening the scope of classical inequalities.

Findings

Derived new weighted anisotropic Hardy inequalities.

Established Rellich type inequalities with boundary terms.

Unified various known inequalities under a general framework.

Abstract

In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new as well as many of the fundamental Hardy and Rellich type inequalities which are known in different settings.