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\( {\mathfrak{B}}_1 \) classes of De Giorgi, Ladyzhenskaya, and Ural’tseva and their application to elliptic and parabolic equations with nonstandard growth

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The article provides an application of the generalized De Giorgi functional classes to the proof of the HÖlder continuity of weak solutions to quasilinear elliptic and parabolic equations with nonstandard growth conditions.

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  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine

    Igor I. Skrypnik & Mykhailo V. Voitovych

  2. Vasyl’ Stus Donetsk National University, Vinnytsia, Ukraine

    Igor I. Skrypnik

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  1. Igor I. Skrypnik
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Correspondence to Igor I. Skrypnik.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 3, pp. 403–447 July–September, 2019.

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Skrypnik, I.I., Voitovych, M.V. \( {\mathfrak{B}}_1 \) classes of De Giorgi, Ladyzhenskaya, and Ural’tseva and their application to elliptic and parabolic equations with nonstandard growth. J Math Sci 246, 75–109 (2020). https://doi.org/10.1007/s10958-020-04724-1

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