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On estimates for volume and surface potentials in domains with boundary of class W l2

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Abstract

We prove sharp estimates in the norms of the Sobolev-Slobodetskii space W l2 , l > 0, for volume and surface potentials in domains with boundary of Sobolev class. The estimates are used in the study of some problems in hydrodynamics for self-gravitating fluids. Bibliography: 4 titles.

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References

  1. N. M. Günter, Potential Theory and Its Applications to Basic Problems of Mathematical Physics [in Russian], Moscow, 1953; English transl.: Ungar, New York, 1968.

  2. L. N. Slobodetskii, “Generalized S. L. Sobolev spaces and their applications to boundary value problems for partial differential equations” [in Russian], Uchen. Zap. Leningr. Herzen Ped. Inst. 197 (1958), 54–112.

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  4. G. Grubb and V. A. Solonnikov, “Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods,” Math. Scand. 69 (1991), 217–290.

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Authors and Affiliations

  1. Steklov Institute of Mathematics in St. Petersburg, Russia, St. Petersburg, Russia

    V. A. Solonnikov

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  1. V. A. Solonnikov
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Correspondence to V. A. Solonnikov.

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Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 93–111.

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Solonnikov, V.A. On estimates for volume and surface potentials in domains with boundary of class W l2 . J Math Sci 150, 1890–1916 (2008). https://doi.org/10.1007/s10958-008-0104-2

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  • DOI: https://doi.org/10.1007/s10958-008-0104-2

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