A div-curl inequality for orthonormal functions

TL;DR

This paper establishes a new inequality relating curl-free and divergence-free vector fields, demonstrating a sublinear bound under orthonormality conditions, akin to Lieb--Thirring inequalities, with potential applications in mathematical analysis.

Contribution

It introduces a novel div-curl inequality for orthonormal functions, extending classical bounds with sublinear scaling properties.

Findings

Bound on sum of products of curl-free and divergence-free fields

Sublinear scaling under orthonormality conditions

Similarity to Lieb--Thirring inequalities

Abstract

We prove a bound on the sum of the product of curl-free and divergence-free vector fields. Under appropriate orthonormality conditions our bound scales sublinearly in the number of terms, similar in spirit to Lieb--Thirring inequalities.