## Rocky Mountain Journal of Mathematics

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

#### Abstract

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

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

Dates
First available in Project Euclid: 14 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1544756816

Digital Object Identifier
doi:10.1216/RMJ-2018-48-7-2431

Mathematical Reviews number (MathSciNet)
MR3892139

Zentralblatt MATH identifier
06999269

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

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1544756816

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