Positivity and strong ellipticity
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.
|Collections||ANU Research Publications|
|Source:||Proceedings of the American Mathematical Society|
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