# On minimal decay at infinity of Hardy-weights

## TL;DR

This paper investigates the decay properties of Hardy-weights for p-Laplacian type operators, establishing sharp conditions at infinity based on integrability, with extensions to nonsymmetric linear elliptic operators and practical applications.

## Contribution

It provides necessary sharp decay conditions for Hardy-weights at infinity and extends results to nonsymmetric linear elliptic operators.

## Key findings

- Derived sharp decay conditions for Hardy-weights at infinity
- Extended decay results to nonsymmetric linear elliptic operators
- Discussed applications to various elliptic operator examples

## Abstract

We study the behaviour of Hardy-weights for a class of variational quasi-linear elliptic operators of $p$-Laplacian type. In particular, we obtain necessary sharp decay conditions at infinity on the Hardy-weights in terms of their integrability with respect to certain integral weights. Some of the results are extended also to nonsymmetric linear elliptic operators. Applications to various examples are discussed as well.