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

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Abstract

An extension of the lower-bound lemma of Boggio is given for the weak forms of certain elliptic operators, which are in general nonlinear and have partially Dirichlet and partially Neumann boundary conditions. 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.

MSC

35P15
35P30

Keywords

Neumann boundary conditions
Hardy in equality
Spectral geometry

Cited by (0)

This work was supported by NSF Grant DMS-0204059.