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A priori estimates of solutions of linear parabolic problems with coefficients from Sobolev spaces

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Abstract

We consider the general initial-boundary-value problem for a linear parabolic equation of arbitrary even order in anisotropic Sobolev spaces. We prove the existence and uniqueness of a solution and establish ana priori estimate for it.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    I. V. Skrypnyk

  2. Kiev University, Kiev

    I. B. Romanenko

Authors
  1. I. V. Skrypnyk
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  2. I. B. Romanenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1534–1548, November, 1999.

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Skrypnyk, I.V., Romanenko, I.B. A priori estimates of solutions of linear parabolic problems with coefficients from Sobolev spaces. Ukr Math J 51, 1733–1748 (1999). https://doi.org/10.1007/BF02525259

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  • DOI: https://doi.org/10.1007/BF02525259

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