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Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

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Abstract

The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.

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Acknowledgements

The first named author was supported by the research grant ARC DP140100649 from the Australian Research Council and Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under Project 101.02–2016.25. The second named author was supported by the research grant ARC DP140100649.

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Authors and Affiliations

  1. Department of Mathematics, Macquarie University, Sydney, NSW, 2109, Australia

    The Anh Bui & Xuan Thinh Duong

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  1. The Anh Bui
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  2. Xuan Thinh Duong
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Correspondence to Xuan Thinh Duong.

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Communicated by L. Caffarelli.

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Bui, T.A., Duong, X.T. Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains. Calc. Var. 56, 177 (2017). https://doi.org/10.1007/s00526-017-1273-y

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