On a Nonlinear Dirichlet Eigenvalue Problem
摘要
In this work, considering a mixed operator composed of the p-Laplacian and the Laplacian, we study a generalized spectral problem with Dirichlet conditions. First, we show the existence of a continuous family of eigenvalues and study some properties of the first eigenvalue and the associated eigenfunctions. Then, using Schwarz symmetrization and p-harmonic transplantation techniques, we show two isoperimetric inequalities, one of which is of Faber-Krahn type.