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Positivity and strong ellipticity

ter Elst, A. F. M.; Robinson, Derek W.; Zhu, Yueping

Description

We consider partial differential operators H = − div(C∇) in divergence form on Rᵈ with a positive-semidefinite, symmetric, matrix C of real L∞-coefficients, and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.

CollectionsANU Research Publications
Date published: 2006-09-28
Type: Journal article
URI: http://hdl.handle.net/1885/100432
Source: Proceedings of the American Mathematical Society
DOI: 10.1090/S0002-9939-05-08180-3

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