Positivity and strong ellipticity

Abstract

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. Show more