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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the Dirichlet problem for the Stokes system in Lipschitz domains
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by Zhong Wei Shen PDF
Proc. Amer. Math. Soc. 123 (1995), 801-811 Request permission

Abstract:

We study the ${L^p}$ Dirichlet problem for the Stokes system in Lipschitz domains. Optimal estimates are obtained when the dimension $n = 3$. In the case of $n \geq 4$, we establish a weak estimate of solutions for certain range of p.
References
  • Björn E. J. Dahlberg and Carlos E. Kenig, Hardy spaces and the Neumann problem in $L^p$ for Laplace’s equation in Lipschitz domains, Ann. of Math. (2) 125 (1987), no. 3, 437–465. MR 890159, DOI 10.2307/1971407
  • —, ${L^p}$ estimates for the three-dimension system of elastostatics on Lipschitz domains, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990. B. Dahlberg, C. Kenig, J. Pipher, and G. Verchota, Area integral estimates and maximum principles for higher order elliptic equations and systems on Lipschitz domains, preprint.
  • B. E. J. Dahlberg, C. E. Kenig, and G. C. Verchota, Boundary value problems for the systems of elastostatics in Lipschitz domains, Duke Math. J. 57 (1988), no. 3, 795–818. MR 975122, DOI 10.1215/S0012-7094-88-05735-3
  • Eugene Fabes, Layer potential methods for boundary value problems on Lipschitz domains, Potential theory—surveys and problems (Prague, 1987) Lecture Notes in Math., vol. 1344, Springer, Berlin, 1988, pp. 55–80. MR 973881, DOI 10.1007/BFb0103344
  • E. B. Fabes, C. E. Kenig, and G. C. Verchota, The Dirichlet problem for the Stokes system on Lipschitz domains, Duke Math. J. 57 (1988), no. 3, 769–793. MR 975121, DOI 10.1215/S0012-7094-88-05734-1
  • M. Giaquinta and G. Modica, Nonlinear systems of the type of the stationary Navier-Stokes system, J. Reine Angew. Math. 330 (1982), 173–214. MR 641818
  • David Jerison and Carlos E. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains, J. Funct. Anal. 130 (1995), no. 1, 161–219. MR 1331981, DOI 10.1006/jfan.1995.1067
  • V. G. Maz’ya and V. A. Plamenvskii, On properties of solutions of three-dimensional problems of elasticity theory and hydrodynamics in domains with isolated singular points, Amer. Math. Soc. Transl. Ser. 2, vol. 123, Amer. Math. Soc., Providence, RI, 1984, pp. 109-123.
  • Jill Pipher and Gregory Verchota, The Dirichlet problem in $L^p$ for the biharmonic equation on Lipschitz domains, Amer. J. Math. 114 (1992), no. 5, 923–972. MR 1183527, DOI 10.2307/2374885
  • Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 801-811
  • MSC: Primary 35Q30; Secondary 76D07
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1223521-9
  • MathSciNet review: 1223521