# Rellich inequalities in bounded domains

## TL;DR

This paper establishes precise conditions for weighted Rellich inequalities in bounded domains, considering various operators and boundary behaviors, including critical cases and remainders.

## Contribution

It provides necessary and sufficient conditions for Rellich inequalities in bounded domains for a class of differential operators, extending previous results.

## Key findings

- Conditions for validity of Rellich inequalities derived
- Analysis of critical cases and boundary behaviors conducted
- Inclusion of remainder terms in inequalities

## Abstract

We find necessary and sufficient conditions for the validity of weighted Rellich inequalities in Lp for functions in bounded domains vanishing at the boundary. General operators like L = Delta+ c\|x|^2x nabla-b\|x|^2 are considered. Critical cases and remainder terms are also investigated.