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

By Francesco Pietra, Nunzia Gavitone. 2012

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In this paper we prove a sharp upper bound for the first Dirichlet eigenvalue of a class of nonlinear elliptic operators which includes the operator Δpu=∑i∂∂xi|∇u|p−2∂u∂xi , that is the p‐Laplacian, and Δ̃pu=∑i∂∂xi|∂u∂xi|p−2∂u∂xi , namely the pseudo‐p‐Laplacian. Moreover we prove a stability result by means of a suitable isoperimetric deficit. Finally, we give a sharp lower bound for the anisotropic p‐torsional rigidity.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/60d1391dfcf841bab6dc031242b2577114dc3202