Towards a refined estimate for topological degree in one dimension

TL;DR

This paper proves a new inequality related to the topological degree of circle maps, inspired by Brezis' conjecture, providing a refined estimate based on nonlocal integrals.

Contribution

It introduces a novel inequality that bounds the topological degree using nonlocal integral estimates, advancing understanding of circle maps.

Findings

Established a new inequality for topological degree

Connected degree bounds to nonlocal integral estimates

Provides a refined estimate inspired by Brezis' conjecture

Abstract

In this paper we prove an inequality inspired by a conjecture of Brezis, which asks for a bound for the topological degree of a map from the circle to itself in terms of a nonlocal integral.