Low perturbations for a class of nonuniformly elliptic problems
Anouar Bahrouni, Du\v{s}an D. Repov\v{s}
TL;DR
This paper introduces a new functional inspired by variable exponent inequalities and investigates its properties and associated eigenvalue problems, expanding understanding of nonuniformly elliptic equations.
Contribution
It presents a novel functional tailored for nonuniformly elliptic problems and analyzes its eigenvalue problem, advancing the mathematical framework in this area.
Findings
Development of a new functional for nonuniformly elliptic problems
Analysis of eigenvalue problems involving the new functional
Extension of variable exponent inequality applications
Abstract
We introduce and study a new functional which was motivated by our paper on the Caffarelli-Kohn-Nirenberg inequality with variable exponent (Bahrouni, R\u{a}dulescu and Repov\v{s}, Nonlinearity 31 (2018), 1518-1534). We also study the eigenvalue problem for equations involving this new functional.
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