Gaussian estimates for degenerate diffusion

Chovanec, Michal

doi:10.1090/S0002-9939-2012-11313-9

Gaussian estimates for degenerate diffusion
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Proc. Amer. Math. Soc. 140 (2012), 3947-3957 Request permission

Abstract:

We prove estimates of Gaussian type for the kernel of the semigroup associated to the operator $m\triangle$, where $m$ is a positive function which may vanish at the boundary (and thus the operator may not be strongly elliptic). No regularity conditions either on the boundary of the domain or on the function $m$ are posed. The optimality of the growth condition on $m$ is discussed.

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