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L p -Estimates for a Linear Problem Arising in the Study of the Motion of an Isolated Liquid Mass

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We prove L p -estimates for solutions of a linear problem arising as a result of linearization of a free boundary problem for a viscous capillary drop. The proof is rather elementary; it is based on the explicit representation formula for the solution of a model problem in the half-space and on the theorem on L p -multipliers in the Fourier integrals. Bibliography: 20 titles.

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  1. St. Petersburg Department of the Steklov Mathematical Institute RAS, 27, Fontanka Str., St. Petersburg, 191023, 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 69, March 2013, pp. 137–166.

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Solonnikov, V.A. L p -Estimates for a Linear Problem Arising in the Study of the Motion of an Isolated Liquid Mass. J Math Sci 189, 699–733 (2013). https://doi.org/10.1007/s10958-013-1214-z

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