Bounds on the Principal Frequency of the ๐-Laplacian
Guillaume Poliquin ยท Contemporary mathematics - American Mathematical Society ยท 2014
This paper is concerned with the lower bounds for the principal frequency of the p p -Laplacian on n 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 โ 2 p eq 2 . As a by-product, we obtain a lower bound on the size of the nodal set of an eigenfunction of the p p -Laplacian on planar domains.