Rocky Mountain Journal of Mathematics

Optimal Morrey estimate for parabolic equations in divergence form via Green's functions

Junjie Zhang and Shenzhou Zheng

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This paper presents a local Morrey regularity with the optimal exponents for linear parabolic equations in divergence form under the assumption that the leading coefficient is independent of $t$ and not necessarily symmetric based on a rather different approach. Here, we achieve it by applying natural growth properties of Green's functions through the use of parabolic operators and the hole-filling technique.

Article information

Rocky Mountain J. Math., Volume 48, Number 7 (2018), 2431-2457.

First available in Project Euclid: 14 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35D30: Weak solutions 35K10: Second-order parabolic equations

Green's function Morrey regularity parabolic equations Gaussian estimates hole-filling technique


Zhang, Junjie; Zheng, Shenzhou. Optimal Morrey estimate for parabolic equations in divergence form via Green's functions. Rocky Mountain J. Math. 48 (2018), no. 7, 2431--2457. doi:10.1216/RMJ-2018-48-7-2431.

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