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Partial applicability of Moser's method to nonlinear elliptic systems

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Abstract

We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutionsu ∈W 1p . It is proved thatDu ∈L q with someq ∈ (p; +∞) and it is explicitly shown howq depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds.

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Authors and Affiliations

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

    E. A. Kalita

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  1. E. A. Kalita
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Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 547–557, October, 1995.

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Kalita, E.A. Partial applicability of Moser's method to nonlinear elliptic systems. Math Notes 58, 1057–1065 (1995). https://doi.org/10.1007/BF02305094

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  • DOI: https://doi.org/10.1007/BF02305094

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