高斯估计：简史
Gaussian Estimates: A Brief History
摘要：
二阶线性抛物型微分方程基本解的双边Gauss估计是关于经典热传导方程基本解的下界.在他的开创性的1958年纳什指出，没有证明，双边非高斯界的基本解的一致抛物发散结构方程假设只有有界的系数。在他1967年至1968年的论文阿伦森得出真正的高斯估计的基本解的一大类线性抛物型方程（包括发散结构方程）根据最小的非正则性假设的系数。随后在1986年Fabes & Stroock得出高斯估计的分歧结构方程直接从纳什的想法，并继续证明纳什的连续性定理和Harnack不等式的后果，他们的估计。在本说明中，我描述这些结果连同各种扩展。
英文摘要：
Two-sided Gaussian estimates for the fundamental solution of a second order linear parabolic differential equation are upper and lower bounds in terms of the fundamental solution of the classical heat conduction equation. In his seminal 1958 paper Nash stated, without proof, two-sided non-Gaussian bounds for the fundamental solution of a uniformly parabolic divergence structure equation assuming only boundedness of the coefficients. In his 1967-1968 papers Aronson derived truly Gaussian estimates for the fundamental solutions of a large class of linear parabolic equations (including the divergence structure equation) under minimal non-regularity assumptions on the coefficients. Subsequently in 1986 Fabes & Stroock derived Gaussian estimates for the divergence structure equation directly from the ideas of Nash and went on to prove Nash's continuity theorem and the Harnack inequality as a consequence of their estimate. In this note I describe these results together with various extensions.
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