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

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

2004-07-27

arxiv.org/abs/math/0407465v1

Mathematics

Spectral Theory

Scientific paper

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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