Rayleigh Principle for Stratified Laplacian

Abstract

In this paper we give an exact analog of Rayleigh principle for laplacians on stratified sets. Our main result may be applied for an estimation of the first eigenvalue of stratified laplacian equipped with Dirichlet conditon. Previous results on this subject were known for one dimensional stratified sets and for a specific laplacian, called 'soft laplacian', defined on multidimensional stratified sets. Meanwhile there is a variety of laplacians on stratified sets. Our results are valid for all stratified laplacians without any restrictions on the dimension.