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Ukrainian Mathematical Journal

, Volume 58, Issue 11, pp 1717–1733 | Cite as

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

  • A. A. Kovalevskii
  • M. V. Voitovich
Article

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.

Keywords

Generalize Solution Fourth Order Dirichlet Problem Monotone Operator Entropy Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. A. Kovalevskii
    • 1
  • M. V. Voitovich
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian Academy of SciencesDonetsk

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