Lower bounds for fractional Orlicz-type eigenvalues

Ariel Salort

Vol. 339 (2025), No. 2, 309–331

DOI: 10.2140/pjm.2025.339.309

Abstract

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 do not assume that $A$ or its complementary function satisfies the ${\mathrm{\Delta }}_2$ condition.

Keywords

eigenvalues, nonlocal, fractional Orlicz–Sobolev, lower bound

Mathematical Subject Classification

Primary: 35P20, 46E30, 35R11, 47J10

Milestones

Received: 4 May 2025

Revised: 20 August 2025

Accepted: 20 August 2025

Published: 21 September 2025