Pointwise Lower bounds on the Heat Kernels of Uniformally Elliptic Operators in Bounded Regions

Details Pointwise Lower bounds on the Heat Kernels of Uniformally Elliptic Operators in Bounded Regions Pointwise Lower bounds on the Heat Kernels of Uniformally Elliptic Operators in Bounded Regions

2011-10-14

arxiv.org/abs/1110.3343v1

Mathematics

Spectral Theory

Scientific paper

We obtain pointwise lower bounds for heat kernels of higher order
differential operators with Dirichlet boundary conditions on bounded domains in
$\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the
heat kernel close to the boundary. We make no smoothness assumptions on our
operator coefficients which we assume only to be bounded and measurable.

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