Geometric lower bounds for the spectrum of elliptic PDEs with Dirichlet conditions in part

2004/07/27 by Evans M. Harrell, Harrell, Evans M.
Mathematics · #35P15 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:35P15

paper · pdf · doi:10.48550/arxiv.math/0407465

arxiv created 2004/07/27 · arxiv updated 2009/12/01

Abstract

An extension of the lower-bound lemma of Boggio is given for the weak forms of certain elliptic operators, which have partially Dirichlet and partially Neumann boundary conditions, and are in general nonlinear. Its consequences and those of an adapted Hardy inequality for the location of the bottom of the spectrum are explored in corollaries wherein a variety of assumptions are placed on the shape of the Dirichlet and Neumann boundaries.

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