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Gradient estimates for parabolic equations in generalized weighted Morrey spaces

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Abstract

We consider the Cauchy–Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain. The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others. We obtain Calderón–Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight.

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Authors and Affiliations

  1. Department of Mathematics, Ahi Evran University, Kirsehir, Turkey

    Vagif Guliyev

  2. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, B. Vahabzade St. 9, Baku, AZ 1141, Azerbaijan

    Vagif Guliyev, Shamsiyya Muradova & Mehriban Omarova

  3. Department of Civil Engineering, Design, Construction and Environment, Second University of Naples, Via Roma 9, 81031, Aversa, Italy

    Lubomira Softova

Authors
  1. Vagif Guliyev
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  2. Shamsiyya Muradova
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  3. Mehriban Omarova
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  4. Lubomira Softova
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Corresponding author

Correspondence to Vagif Guliyev.

Additional information

The research of V. Guliyev, Sh. A. Muradova and M. Omarova is partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015; the research of L. Softova is partially supported by the grant INDAM-GNAMPA Project 2015

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Guliyev, V., Muradova, S., Omarova, M. et al. Gradient estimates for parabolic equations in generalized weighted Morrey spaces. Acta. Math. Sin.-English Ser. 32, 911–924 (2016). https://doi.org/10.1007/s10114-016-5530-3

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  • DOI: https://doi.org/10.1007/s10114-016-5530-3

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