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Transactions of the American Mathematical Society

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On the Cauchy problem for stochastic parabolic equations in Hölder spaces


Authors: Kai Du and Jiakun Liu
Journal: Trans. Amer. Math. Soc. 371 (2019), 2643-2664
MSC (2010): Primary 35R60, 60H15
DOI: https://doi.org/10.1090/tran/7533
Published electronically: November 27, 2018
MathSciNet review: 3896092
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Abstract: In this paper, we establish a sharp $ C^{2+\alpha }$-theory for stochastic partial differential equations of parabolic type in the whole space.


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Additional Information

Kai Du
Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales 2522, Australia
Address at time of publication: Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200438, China
Email: kdu@fudan.edu.cn

Jiakun Liu
Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales 2522, Australia
Email: jiakunl@uow.edu.au

DOI: https://doi.org/10.1090/tran/7533
Keywords: Stochastic PDE, Schauder estimate, H\"older space
Received by editor(s): March 17, 2016
Received by editor(s) in revised form: May 18, 2017, and September 25, 2017
Published electronically: November 27, 2018
Additional Notes: The research of the first author was partially supported by National Science Foundation of China No.11801084
The research of the second author was supported by the Australian Research Council DE140101366
The second author is the corresponding author
Article copyright: © Copyright 2018 American Mathematical Society