A proof of the Faber-Krahn inequality for the first eigenvalue of the \(p\)-Laplacian

DOI10.1007/BF02505910zbMath0966.35091OpenAlexW2026929913MaRDI QIDQ1570434

Tilak Bhattacharya

Publication date: 16 August 2001

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02505910

zbMATH Keywords

\(p\)-LaplacianFaber-Krahn inequalityproperties of the first eigenfunctionTalenti's inequality

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Estimates of eigenvalues in context of PDEs (35P15)

Related Items

The Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet \(p\)-Laplacian for triangles and quadrilaterals ⋮ Domain variations of the first eigenvalue via a strict Faber-Krahn type inequality ⋮ Some stability estimates for the symmetrized first eigenfunction of certain elliptic operators ⋮ Faber-Krahn inequality for Robin problems involving \(p\)-Laplacian ⋮ Lower bounds for generalized eigenvalues of the quasilinear systems ⋮ Faber–Krahn inequalities for Schrödinger operators with point and with Coulomb interactions ⋮ On the Faber–Krahn inequality for the Dirichletp-Laplacian ⋮ Estimates for eigenvalues of quasilinear elliptic systems ⋮ From affine Poincaré inequalities to affine spectral inequalities ⋮ Isoperimetric inequalities for eigenvalues by inverse mean curvature flow ⋮ A Faber-Krahn inequality for the Riesz potential operator for triangles and quadrilaterals

Cites Work

• Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces
• Regularity for a more general class of quasilinear equations
• Some estimates for the symmetrized first eigenfunction of the Laplacian
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Some results concerning the eigenvalue problem for the p-Laplacian
• Boundary regularity for solutions of degenerate elliptic equations
• Addendum to On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0"
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