A Faber-Krahn inequality for nonhomogeneous wedge-like membranes

Abdelhalim Hasnaoui; Abdelhamid Zaghdani; Abdelhalim Hasnaoui; Abdelhamid Zaghdani

doi:10.3934/math.2025543

AIMS Mathematics

2025, Volume 10, Issue 5: 11988-11997. doi: 10.3934/math.2025543

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Research article

A Faber-Krahn inequality for nonhomogeneous wedge-like membranes

Mathematics Department, College of Sciences and Arts, Northern Border University, Rafha, Saudi Arabia

Received: 02 November 2024 Revised: 12 April 2025 Accepted: 21 April 2025 Published: 23 May 2025
MSC : 35P15, 58E30

In this paper, we adapt B. Schwarz and Banks-Krein techniques to obtain a new version of Faber-Krahn inequality for the first Dirichlet eigenvalue of the Laplacian in wedge like membranes with continuous mass density function.
- Dirichlet eigenvalues,
- wedge-like membranes,
- Faber-Krahn inequality,
- weighted symmetrization,
- Rayleigh quotient
Citation: Abdelhalim Hasnaoui, Abdelhamid Zaghdani. A Faber-Krahn inequality for nonhomogeneous wedge-like membranes[J]. AIMS Mathematics, 2025, 10(5): 11988-11997. doi: 10.3934/math.2025543

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Abstract

In this paper, we adapt B. Schwarz and Banks-Krein techniques to obtain a new version of Faber-Krahn inequality for the first Dirichlet eigenvalue of the Laplacian in wedge like membranes with continuous mass density function.

References

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