Monotonicity with respect to \(p\) of the first nontrivial eigenvalue of the \(p\)-Laplacian with homogeneous Neumann boundary conditions

DOI10.3934/cpaa.2020198zbMath1465.35327OpenAlexW3037742629MaRDI QIDQ2658635

Mihai Mihăilescu, Julio D. Rossi

Publication date: 23 March 2021

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2020198

zbMATH Keywords

Neumann boundary condition\(p\)-Laplacianconvex domainfirst positive eigenvalue

Mathematics Subject Classification ID

Variational inequalities (49J40) Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Spectral theory; eigenvalue problems on manifolds (58C40) Variational methods for eigenvalues of operators (49R05) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (4)

Monotonicity properties for the variational Dirichlet eigenvalues of the \(p\)-Laplace operator ⋮ The monotonicity of the \(p\)-torsional rigidity in convex domains ⋮ The equality case in Cheeger's and Buser's inequalities on \(\mathsf{RCD}\) spaces ⋮ On the monotonicity of the best constant of Morrey’s inequality in convex domains

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