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Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials

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Abstract

For parabolic equations with nonstandard growth conditions, we prove local boundedness of weak solutions in terms of nonlinear parabolic potentials of the right-hand side of the equation.

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Authors and Affiliations

  1. Kateryna Oleksandrivna Buryachenko Vasyl’ Stus Donetsk National University, Vinnytsia, Ukraine

    Kateryna O. Buryachenko

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  1. Kateryna O. Buryachenko
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Correspondence to Kateryna O. Buryachenko.

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Dedicated to the memory of Professor Bogdan Bojarski

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 1, pp. 28–45 January–March, 2019.

This work is supported by grants of the Ministry of Education and Science of Ukraine, projects 0118U003138 and 0119U100421.

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Buryachenko, K.O. Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials. J Math Sci 242, 772–786 (2019). https://doi.org/10.1007/s10958-019-04515-3

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  • DOI: https://doi.org/10.1007/s10958-019-04515-3

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