The limit as $p\to 1$ of the higher eigenvalues of the $p$-Laplacian operator $\Delta_p$

DOI10.1512/iumj.2021.70.8563zbMath1480.35307OpenAlexW3196857561MaRDI QIDQ3380486

Sergio Segura de León, José C. Sabina De Lis

Publication date: 29 September 2021

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2021.70.8563

zbMATH Keywords

radial solutionsfunctions of bounded variation1-Laplacian operatorLjusternik-Schnirelman (Dirichlet) eigenvalues

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Optimality conditions for problems involving ordinary differential equations (49K15) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Variational methods for eigenvalues of operators (49R05) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (5)

Monotonicity properties for the variational Dirichlet eigenvalues of the \(p\)-Laplace operator ⋮ Asymptotic behavior and monotonicity of radial eigenvalues for the \(p\)-Laplacian ⋮ The convective eigenvalues of the one-dimensional \(p\)-Laplacian as \(p\rightarrow 1\) ⋮ Gelfand-type problems involving the 1-Laplacian operator ⋮ \(p\)-Laplacian diffusion coupled to logistic reaction: asymptotic behavior as \(p\) goes to 1. To the memory of Professor Ireneo Peral Alonso, a brilliant mathematician, excellent person and dear friend

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