Positivity and strong ellipticity
A. F. M. ter Elst, Derek W. Robinson, Yueping Zhu
Abstract
We consider second-order partial differential operators H in divergence form on d 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.
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