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Eigenvalues of the Neumann Laplacian with Density and Sharp Sobolev–Orlicz Embeddings

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We provide estimates for the constant in the weighted Sobolev–Poincaré inequality for a special class of planar domains and weights. We obtain lower bounds for the first nonzero eigenvalue μρ of the Neumann Laplacian with density ρ. These estimates depend on the density function and geometry of the domain. We show that μρ can be made arbitrarily large by changing the mass density of the domain.

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  1. Ben-Gurion University of the Negev, P.O.Box 653, 8410501, Beer Sheva, Israel

    Alexander Menovschikov

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  1. Alexander Menovschikov
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Correspondence to Alexander Menovschikov.

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Menovschikov, A. Eigenvalues of the Neumann Laplacian with Density and Sharp Sobolev–Orlicz Embeddings. J Math Sci 281, 782–804 (2024). https://doi.org/10.1007/s10958-024-07147-4

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