Gaussian Estimates for Fundamental Solutions of Second Order Parabolic Systems with Time-independent Coefficients
نویسنده
چکیده
Abstract. Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on Rn. In particular, in the case when n = 2 they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded, measurable, time-independent coefficients, and extend their results to the systems of parabolic equations.
منابع مشابه
A Note on Heat Kernel Estimates for Second-order Elliptic Operators
We study fundamental solutions to second order parabolic systems of divergence type with time independent coefficients, and give another proof of a result by Auscher, McIntosh and Tchamitchian on the Gaussian bounds for the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients.
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