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On the boundedness of generalized solutions of higher-order nonlinear elliptic equations with data from an Orlicz–Zygmund class

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Abstract

In the present paper, a 2mth-order quasilinear divergence equation is considered under the condition that its coefficients satisfy the Carathéodory condition and the standard conditions of growth and coercivity in the Sobolev space W m,p(Ω), Ω ⊂ Rn, p > 1. It is proved that an arbitrary generalized (in the sense of distributions) solution u ∈ W m,p0 (Ω) of this equation is bounded if m ≥ 2, n = mp, and the right-hand side of this equation belongs to the Orlicz–Zygmund space L(log L)n−1(Ω).

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine

    M. V. Voitovich

  2. Mariupol State University, Mariupol, Ukraine

    M. V. Voitovich

  3. Donetsk National University, Vinnitsa, Ukraine

    M. V. Voitovich

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  1. M. V. Voitovich
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Correspondence to M. V. Voitovich.

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Original Russian Text © M. V. Voitovich, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 6, pp. 855–866.

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Voitovich, M.V. On the boundedness of generalized solutions of higher-order nonlinear elliptic equations with data from an Orlicz–Zygmund class. Math Notes 99, 840–850 (2016). https://doi.org/10.1134/S0001434616050229

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  • DOI: https://doi.org/10.1134/S0001434616050229

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