I look for a book or a paper about the first eigenvalue of the $-\Delta_p$ operator. To be more precise, I am interested in understanding what is the relation between the first eigenvalue of the $-\Delta_p$ and the first eigenvalue of the $-\Delta_q$ laplacian when $p<q$ (I mean, it becomes greater, smaller or nothing can be said?)
Could anyone help me, please? Thank you in advance!
The following notes (https://folk.ntnu.no/lqvist/p-laplace.pdf) contain the definition of $\Delta_p$ for various values of $p$.
The following slides (http://benasque.org/2019pde/talks_contr/268_Farid_Benasque_2.pdf) contain a statement of the first and higher eigenvalue problem for the $p$-Laplace operators, relationships between the eigenvalues at various $p$'s and further references.