Abstract
The boundary regularity of solutions to some boundary-value problems describing stationary flow of generalized Newtonian liquids is studied. The dissipative potential is of quadratic growth at infinity. We prove that the second-order derivatives of the solution are pth power summable functions, where p is greater than two. The partial regularity of the strain velocity tensor is established. In the two-dimensional case, the complete regularity of the strain velocity tensor is also proved. Bibliography: 14 titles.
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Translated fromProblemy Matematicheskogo Analiza, No. 18, 1998, pp. 222–246.
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Shilkin, T.N. Estimate for the second-order derivatives of solutions to boundary-value problems of the theory of non-Newtonian liquids. J Math Sci 98, 781–797 (2000). https://doi.org/10.1007/BF02355390
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DOI: https://doi.org/10.1007/BF02355390