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A sharp pointwise bound for functions with $L^2$-Laplacians on arbitrary domains and its applications
Author(s):
Wenzheng
Xie
Journal:
Bull. Amer. Math. Soc.
26
(1992),
294-298.
MSC (2000):
Primary 26D10, 35B45, 35Q20
MathSciNet review:
1126088
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References:
- *
- {hera}J. G. Heywood and R. Rannacher, {\em Finite element approximation of the nonstationary Navier-Stokes problem.}I. {\em Regularity of solutions and second-order error estimates for spatial discretization}, SIAM J. Numer. Anal. {\bf 19} (1982), 275--311. MR 650052
- *
- {te}R. Temam, {\em Navier-Stokes equations and nonlinear functional analysis}, SIAM, Philadelphia, PA, 1983. MR 764933
- *
- {adfo}R. A. Adams and J. J. Fournier, {\em Cone conditions and properties of Sobolev spaces}, J. Math. Anal. Appl. {\bf 61} (1977), 713--734. MR 463902
- *
- {la}O. A. Ladyzhenskaya, {\em The boundary value problems of mathematical physics}, Appl. Math. Sci., vol. 49, Springer-Verlag, New York,1985. MR 793735
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- {gr}P. Grisvard, {\em Elliptic problems in nonsmooth domains}, Monographs Stud. Math., vol. 24, Pitman Publishing Inc., Boston, MA, 1985. MR 775683
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- {he}J. G. Heywood, {\em The Navier-Stokes equations: on the existence, regularity and decay of solutions}, Indiana Univ. Math. J. {\bf 29} (1980), 639--681. MR 589434
- *
- {xi}W. Xie,{\em A sharp pointwise bound for the Poisson equation in arbitrary domains and its applications to Burgers' equation}, thesis, University of British Columbia, 1991. MR
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00279-3
PII:
S 0273-0979(1992)00279-3
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