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On the improvement of summability of generalized solutions of the Dirichlet problem for nonlinear equations of the fourth order with strengthened ellipticity

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Abstract

We consider the Dirichlet problem for a class of nonlinear divergent equations of the fourth order characterized by the condition of strengthened ellipticity imposed on their coefficients. The main result of the present paper shows how the summability of generalized solutions of the given problem improves, depending on the variation in the exponent of summability of the right-hand side of the equation beginning with a certain critical value. The exponent of summability that guarantees the boundedness of solutions is determined more exactly.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    A. A. Kovalevskii & M. V. Voitovich

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  1. A. A. Kovalevskii
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  2. M. V. Voitovich
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__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 11, pp. 1511–1524, November, 2006.

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Kovalevskii, A.A., Voitovich, M.V. On the improvement of summability of generalized solutions of the Dirichlet problem for nonlinear equations of the fourth order with strengthened ellipticity. Ukr Math J 58, 1717–1733 (2006). https://doi.org/10.1007/s11253-006-0164-8

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  • DOI: https://doi.org/10.1007/s11253-006-0164-8

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