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The spectrum of the mean curvature operator

Part of: Linear function spaces and their duals Spectral theory and eigenvalue problems Existence theories Elliptic equations and systems

Published online by Cambridge University Press:  01 April 2020

Mihai Mihăilescu
Mihai Mihăilescu*
Affiliation:
Department of Mathematics, University of Craiova, 200585Craiova, Romania The Research Institute of the University of Bucharest, University of Bucharest, 050663Bucharest, Romania (mmihailes@yahoo.com)
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Abstract

We show that the spectrum of the relativistic mean curvature operator on a bounded domain Ω ⊂ ℝN (N ⩾ 1) having smooth boundary, subject to the homogeneous Dirichlet boundary condition, is exactly the interval (λ1(2), ∞), where λ1(2) stands for the principal frequency of the Laplace operator in Ω.

Keywords

Eigenvalue problemsΓ-convergenceMean curvature operatorp-LaplacianVariational inequalities

MSC classification

Primary: 35J92: Quasilinear elliptic equations with $p$-Laplacian
Secondary: 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 49J40: Variational methods including variational inequalities 49J45: Methods involving semicontinuity and convergence; relaxation
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 2 , April 2021 , pp. 451 - 463
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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