On the structure of the second eigenfunctions of the $p$-Laplacian on a ball

DOI10.1090/proc/12902zbMath1386.35288arXiv1506.05184OpenAlexW1808587840MaRDI QIDQ2796719

Sarath Sasi, T. V. Anoop, Pavel Drábek

Publication date: 29 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.05184

zbMATH Keywords

nonlinear eigenvalue problem\(p\)-Laplacianvariational characterizationsymmetry propertiesshape derivative

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Variational methods for eigenvalues of operators (49R05) Symmetries, invariants, etc. in context of PDEs (35B06) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (12)

Nonradiality of second eigenfunctions of the fractional Laplacian in a ball ⋮ On multiplicity of eigenvalues and symmetry of eigenfunctions of the \(p\)-Laplacian ⋮ On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli ⋮ Approximation of the second eigenvalue of the \(p\)-Laplace operator in symmetric domains ⋮ A toy Neumann analogue of the nodal line conjecture ⋮ 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 qualitative properties of solutions for elliptic problems with thep-Laplacian through domain perturbations ⋮ On reverse Faber-Krahn inequalities ⋮ Theoretical developments in the study of partial differential equations ⋮ Optimal shapes for the first Dirichlet eigenvalue of the \(p\)-Laplacian and dihedral symmetry ⋮ On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

Cites Work

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• Boundary regularity for solutions of degenerate elliptic equations
• Positive eigenfunctions for the p-Laplace operator revisited
• Monotonicity of the principal eigenvalue of the $p$-Laplacian in an annulus
• Isoperimetric Inequalities and Their Applications
• An eigenvalue optimization problem for the p-Laplacian
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