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On the weak limit of mappings with finite distortion
Author(s):
Baisheng
Yan
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3335-3340.
MSC (1991):
Primary 30C65, 30C70, 49J45
Posted:
May 11, 2000
MathSciNet review:
1676345
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Abstract:
We give a new proof that the limit of a weakly convergent sequence of mappings with finite distortion also has finite distortion. The result has been recently proved by Gehring and Iwaniec using the biting convergence of Jacobians. We present a different proof using simply the lower semi-continuity of quasiconvex functionals.
References:
-
- 1.
- E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal., 86 (1984), 125-145. MR 85m:49021
- 2.
- J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 63 (1977), 337-403. MR 57:14788
- 3.
- F. Gehring and T. Iwaniec, The limit of mappings with finite distortion, Ann. Acad. Sci. Fenn. Math., 24 (1999), 253-264. MR 99m:30041
- 4.
- T. Iwaniec, The failure of lower semicontinuity for the linear dilatation, Bull. London Math. Soc., 30 (1998), 55-61. MR 98i:30033
- 5.
- C. B. Morrey, ``Multiple Integrals in the Calculus of Variations," Springer-Verlag, Berlin, Heidelberg, New York, 1966. MR 34:2380
- 6.
- Yu. G. Reshetnyak, ``Space Mappings with Bounded Distortion," Transl. Math. Mono., Amer. Math. Soc., Vol. 73, 1989. MR 90d:30067
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Additional Information:
Baisheng
Yan
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
yan@math.msu.edu
DOI:
10.1090/S0002-9939-00-05435-6
PII:
S 0002-9939(00)05435-6
Received by editor(s):
September 17, 1998
Received by editor(s) in revised form:
January 11, 1999
Posted:
May 11, 2000
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2000,
American Mathematical Society
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