We obtain Gaussian upper bounds for heat kernels of higher order differentialoperators with Dirichlet boundary conditions on bounded domains in $\R^N$. Thebounds exhibit explicitly the nature of the spatial decay of the heat kernelclose to the boundary as well as the long-time exponential decay implied by thespectral gap. We make no smoothness assumptions on our operator coefficientswhich we assume only to be bounded and measurable Keywords : Heat Kernel, Parabolic, Uniformly Elliptic, Gaussian.
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机译：我们在$ \ R ^ N $的有界域上获得Dirichlet边界条件的高阶微分算子的热核的高斯上限。边界清楚地显示了靠近边界的热核的空间衰减的性质，以及光谱间隙所隐含的长时间指数衰减。我们对算子系数不做任何光滑度假设，我们假设它们只是有界和可测量的。关键词：热核，抛物线，均匀椭圆，高斯。
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