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Applications of multipliers to the problem of coercivity in wp l of the Neumann problem

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Abstract

Theorems are proved on the unique solvability and Fredholm property of the Neumann problem for a second-order elliptic equation with nonsmooth coefficients and boundary of the domain. Conditions are formulated on the coefficients and the boundary in terms of multipliers of a Sobolev space. Easily verifiable sufficient conditions are presented in analytic terms that sharpen the known ones.

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References

  1. V. G. Maz'ya and T. O. Shaposhnikova, Multipliers in Spaces of Differentiable Functions [in Russian], Leningrad State Univ., Leningrad (1986).

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  2. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973).

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Authors
  1. T. O. Shaposhnikova
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Additional information

Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 237–248, 1990.

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Shaposhnikova, T.O. Applications of multipliers to the problem of coercivity in wp l of the Neumann problem. J Math Sci 64, 1381–1388 (1993). https://doi.org/10.1007/BF01098029

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  • DOI: https://doi.org/10.1007/BF01098029

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