Bounds on the Principal Frequency of the $p$-Laplacian
Poliquin, Guillaume · arXiv (Cornell University) · 2013
This paper is concerned with the lower bounds for the principal frequency of the $p$-Laplacian on $n$-dimensional Euclidean domains. In particular, we extend the classical results involving the inner radius of a domain and the first eigenvalue of the Laplace operator to the case $p eq2$. As a by-product, we obtain a lower bound on the size of the nodal set of an eigenfunction of the $p$-Laplacian on planar domains.