The second eigenvalue of the \(p\)-Laplacian as \(p\) goes to 1

DOI10.1155/2010/984671zbMath1207.35235OpenAlexW1536841503WikidataQ58651297 ScholiaQ58651297MaRDI QIDQ606262

Enea Parini

Publication date: 16 November 2010

Published in: International Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/230371

zbMATH Keywords

asymptotic behaviour\(p\)-Laplaciansecond eigenvaluenonradial eigenfunction

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) General topics in linear spectral theory for PDEs (35P05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (16)

On the Hong-Krahn-Szego inequality for the \(p\)-Laplace operator ⋮ Convergence of the eigenvalues of the \(p\)-Laplace operator as \(p\) goes to 1 ⋮ Monotonicity properties for the variational Dirichlet eigenvalues of the \(p\)-Laplace operator ⋮ On multiplicity of eigenvalues and symmetry of eigenfunctions of the \(p\)-Laplacian ⋮ Approximation of the second eigenvalue of the \(p\)-Laplace operator in symmetric domains ⋮ Asymptotic behavior and monotonicity of radial eigenvalues for the \(p\)-Laplacian ⋮ The second eigenfunction of the \(p\)-Laplacian on the disk is not radial ⋮ Necessary condition for eigensolutions of the 1-Laplace operator by means of inner variations ⋮ The homotopy significant spectrum compared to the Krasnoselskii spectrum ⋮ Cheeger sets for rotationally symmetric planar convex bodies ⋮ On the geometry of the \(p\)-Laplacian operator ⋮ On some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the \(p\)-Laplacian on a disk ⋮ On the structure of the second eigenfunctions of the $p$-Laplacian on a ball ⋮ The limit as $p\to 1$ of the higher eigenvalues of the $p$-Laplacian operator $\Delta_p$ ⋮ The Cheeger N-problem in terms of BV functions ⋮ Symmetry breaking in a constrained Cheeger type isoperimetric inequality

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