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Transactions of the American Mathematical Society

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Nondivergence parabolic equations in weighted variable exponent spaces


Authors: Sun-Sig Byun, Mikyoung Lee and Jihoon Ok
Journal: Trans. Amer. Math. Soc. 370 (2018), 2263-2298
MSC (2010): Primary 35K20; Secondary 46E30, 46E35
DOI: https://doi.org/10.1090/tran/7352
Published electronically: November 30, 2017
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Abstract: We prove the global Calderón-Zygmund estimates for second order parabolic equations in nondivergence form in weighted variable exponent Lebesgue spaces. We assume that the associated variable exponent is log-Hölder continuous, the weight is of a certain Muckenhoupt class with respect to the variable exponent, the coefficients of the equation are the functions of small bonded mean oscillation, and the underlying domain is a $ C^{1,1}$-domain.


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Additional Information

Sun-Sig Byun
Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 08826, Korea
Email: byun@snu.ac.kr

Mikyoung Lee
Affiliation: Department of Mathematical Sciences, KAIST, Daejeon 34141, Korea
Email: mikyounglee@kaist.ac.kr

Jihoon Ok
Affiliation: Department of Applied Mathematics and Institute of Natural Science, Kyung Hee University, Yongin 17104, Korea
Email: jihoonok@khu.ac.kr

DOI: https://doi.org/10.1090/tran/7352
Keywords: Parabolic equation, Calder\'on-Zygmund estimate, variable exponent, parabolic Muckenhoupt weight, BMO space
Received by editor(s): May 20, 2015
Published electronically: November 30, 2017
Additional Notes: The first author was supported by the National Research Foundation of Korea (NRF-2017R1A2B2003877). The second author was supported by the National Research Foundation of Korea (NRF-2015R1A4A1041675). The third author was supported by the National Research Foundation of Korea (NRF-2017R1C1B2010328)
Article copyright: © Copyright 2017 American Mathematical Society

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