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Positivity and strong ellipticity

A. F. M. ter Elst·Derek W. Robinson·Yueping Zhu
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Abstract

We consider second-order partial differential operators $H$ in divergence form on $\Ri^d$ with a positive-semidefinite, symmetric, matrix $C$ of real $L_\infty$-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.

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A. F. M. ter Elst, Derek W. Robinson, Yueping Zhu. 2006-01-13. Positivity and strong ellipticity. https://arxiv.org/abs/math/0601347

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