Sharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators

Abstract

We prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the p-Laplace and the pseudo-p-Laplace operators. Moreover, we prove a stability result by means of a suitable isoperimetric deficity. Finally, we give a sharp lower bound for the anisotropic p-torsional rigidity.

References in corpus (2)

• Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials
• Stability results for some fully nonlinear eigenvalue estimates

Cited by in corpus (9)

• Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials
• On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
• Sharp estimates for the anisotropic torsional rigidity and the principal frequency
• A sharp weighted anisotropic Poincaré inequality for convex domains
• On the reverse Faber-Krahn inequalities
• Eigenvalues for a nonlocal pseudo $p-$Laplacian
• A sharp bound for the first Robin-Dirichlet eigenvalue
• Series expansion of weighted Finsler-Kato-Hardy inequalities
• On a weighted anisotropic eigenvalue problem