Lower bounds for fractional Orlicz-type eigenvalues

TL;DR

This paper derives precise lower bounds for eigenvalues of the fractional A-Laplacian operator, linking them to domain geometry and the growth of the Young function without requiring the Δ₂ condition.

Contribution

It provides new lower bounds for fractional Orlicz-type eigenvalues that do not depend on the Δ₂ condition, extending previous results to more general Young functions.

Findings

Lower bounds depend on domain geometry and growth properties of A.

Bounds are valid without assuming Δ₂ condition for A or its complement.

Results apply to a broad class of Young functions.

Abstract

In this article, we establish precise lower bounds for the eigenvalues and critical values associated with the fractional $A-$Laplacian operator, where $A$ is a Young function. The obtained bounds are expressed in terms of the domain geometry and the growth properties of the function $A$. We emphasize that we do not assume that $A$ or its complementary function satisfies the $\Delta_2$ condition.