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首页> 外文期刊>Journal of Functional Analysis >Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form
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Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form

机译：散度形式下高阶椭圆算子和系统的正则定理和热核估计之间的等价关系

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摘要

We study the heat kernel of higher order elliptic operators or systems tinder divergence form on R-n. Ellipticity is in the sense of Garding inequality. We show that for homogeneous operators Gaussian upper bounds and Holder regularity of the heat kernel is equivalent to local regularity of weak solutions, We also show stability of such bounds tinder L-infinity-perturbations of the coefficients or under perturbations with bounded coefficients lower order terms. Such a criterion allows us to obtain heat kernel bounds for operators or systems with uniformly continuous or vmo coefficients. (C) 2000 Academic Press. [References: 33]
机译：我们研究了R-n上高阶椭圆算子或系统火种散度形式的热核。椭圆性是Garding不平等的意思。我们证明了对于热算子的齐次算子高斯上界和Holder正则等价于弱解的局部正则，我们也证明了此类界的稳定性，即系数的L-无穷扰动或有界系数低阶项的扰动。这样的标准使我们能够获得具有均匀连续或vmo系数的算子或系统的热核边界。 （C）2000学术出版社。 [参考：33]

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