Positivity and strong ellipticity

A. F.M. Ter Elst*, Derek W. Robinson, Yueping Zhu

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)707-714
    Number of pages8
    JournalProceedings of the American Mathematical Society
    Volume134
    Issue number3
    DOIs
    Publication statusPublished - Mar 2006

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