Abstract
We consider partial differential operators H = - div(C▽) in divergence form on Rd with a positive-semidefinite, symmetric, matrix C of real Z∞-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.
Original language | English |
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Pages (from-to) | 707-714 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 134 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2006 |