Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator - Concepedia

Concepedia

Publication | Closed Access

Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator

71

Citations

0

References

2002

Year

Adimurthi, K. Sandeep

Proceedings of the Royal Society of Edinburgh Section A Mathematics

Spectral TheoryElliptic EquationEngineeringRiemann-hilbert ProblemPerturbed Hardy-sobolev OperatorPotential TheoryPerturbed Hardy–sobolev OperatorFirst EigenvalueFunctional AnalysisPerturbation QNonlinear Functional Analysis

Abstract

In this paper we study the existence, non-existence and simplicity of the first eigenvalue of the perturbed Hardy-Sobolev operator under various assumptions on the perturbation q . We study the asymptotic behaviour of the first eigenfunction near the origin when the perturbation q is q = s , 0 < s < 1. We will also establish the best constant in a Hardy-Sobolev inequality proved by Adimurthi et al.