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Reduced Hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow
Authors:
Ronald J. DiPerna and Andrew Majda
Journal:
J. Amer. Math. Soc. 1 (1988), 59-95
MSC:
Primary 35Q10; Secondary 76C99
MathSciNet review:
924702
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
Robert
A. Adams, Sobolev spaces, Academic Press [A subsidiary of
Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and
Applied Mathematics, Vol. 65. MR 0450957
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exceptional sets, Indiana Univ. Math. J. 22
(1972/73), 873–905. MR 0320346
(47 #8885)
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Ronald
J. DiPerna and Andrew
J. Majda, Oscillations and concentrations in weak solutions of the
incompressible fluid equations, Comm. Math. Phys. 108
(1987), no. 4, 667–689. MR 877643
(88a:35187)
- [4]
Ronald
J. DiPerna and Andrew
J. Majda, Concentrations in regularizations for 2-D incompressible
flow, Comm. Pure Appl. Math. 40 (1987), no. 3,
301–345. MR
882068 (88e:35149), http://dx.doi.org/10.1002/cpa.3160400304
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Federer and William
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derivatives are 𝑝-th power summable, Indiana Univ. Math. J.
22 (1972/73), 139–158. MR 0435361
(55 #8321)
- [6]
P. L. Lions, The concentration-compactness principle in the calculus of variations: the locally compact case, Parts I and II, Ann. Inst. H. Poincaré, 1984, 109-145 and 223-283.
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-, The concentration-compactness principle in the calculus of variations: the limit case, Parts I and II, Riv. Mat. Iberoamericana I (1984), 145-201 and I (1985), 45-121.
- [8]
Elias
M. Stein, Singular integrals and differentiability properties of
functions, Princeton Mathematical Series, No. 30, Princeton University
Press, Princeton, N.J., 1970. MR 0290095
(44 #7280)
-
- [1]
- R. Adams, Sobolev spaces, Academic Press, New York, 1975. MR 0450957 (56:9247)
- [2]
- R. Adams and N. Meyers, Bessel potentials. Inclusion relations among classes of exceptional sets, Indiana Math. J. 22 (1973), 873-905. MR 0320346 (47:8885)
- [3]
- R. DiPerna and A. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Commun. Math. Phys. 108 (1987), 667-689. MR 877643 (88a:35187)
- [4]
- -, Concentrations in regularizations for
 -D incompressible flow, Comm. Pure Appl. Math. 60 (1987), 301-345. MR 882068 (88e:35149) - [5]
- H. Federer and W. P. Ziemer, The Lebesgue set of a function whose distributional derivatives are pth-power summable, Indiana Univ. Math. J. 22 (1972), 139-158. MR 0435361 (55:8321)
- [6]
- P. L. Lions, The concentration-compactness principle in the calculus of variations: the locally compact case, Parts I and II, Ann. Inst. H. Poincaré, 1984, 109-145 and 223-283.
- [7]
- -, The concentration-compactness principle in the calculus of variations: the limit case, Parts I and II, Riv. Mat. Iberoamericana I (1984), 145-201 and I (1985), 45-121.
- [8]
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, N.J., 1970. MR 0290095 (44:7280)
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Additional Information
Ronald J. DiPerna
Affiliation:
Andrew Majda
Affiliation:
DOI:
http://dx.doi.org/10.1090/S0894-0347-1988-0924702-6
PII:
S 0894-0347(1988)0924702-6
Article copyright:
© Copyright 1988 American Mathematical Society
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