A linear boundary value problem for weakly quasiregular mappings in space

Calculus of Variations and Partial Differential Equations

Volumn 13, Issue 3, 2001, Pages 295-310

  Yan, Baisheng ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013024448     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260000074     Document Type: Article

References (33)

1. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975
2. K. Astala, Analytic aspects of quasiconformality, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 617-626
3. K. Astala, Analytic aspects of quasiconformality, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 617-626
4. J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403
5. J. M. Ball and R. D. James, Proposed experimental tests of a theory of fine microstructures and the two well problem, Phil. Trans. Roy. Soc. London 338A (1992), 389-450
6. 1,p-Quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225-253
7. A. Cellina, On minima of a functional of the gradient: sufficient conditions, Nonlinear Anal. 20 (4) (1993), 343-347
8. B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, New York, 1989
9. B. Dacorogna and P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases, Acta Math. 178 (1) (1997), 1-37
10. B. Dacorogna and P. Marcellini, Cauchy-Dirichlet problem for first order nonlinear systems, J. Funct. Anal. 152 (2) (1998), 404-446
11. M. Gromov, Partial Differential Relations, Springer-Verlag, New York, 1986
12. T. Iwaniec, p-Harmonic tensors and quasiregular mappings, Ann. of Math. (2) 136(3) (1992), 589-624
13. n, Trans. Amer. Math. Soc., to appear
14. T. Iwaniec and A. Lutoborski, Integral estimates for null Lagrangians, Arch. Rational Mech. Anal. 125 (1993), 25-79
15. T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29-81
16. T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. reine angew. Math. 454 (1994), 143-161
17. C. B. Morrey, Quasiconvexity and the lowersemicontinuity of multiple integrals, Pacific J. Math. 2 (1952), 25-53
18. C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966
19. S. Müller and V. Šverák, Attainment results for the two-well problem by convex integration, in Geometric Analysis and the Calculus of Variations, pp. 239-251, Internat. Press, Cambridge, MA, 1996
20. S. Müller and V. Šverák, Unexpected solutions of first and second order partial differential equations, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 691-702
21. S. Müller and V. Šverák, Unexpected solutions of first and second order partial differential equations, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 691-702
22. S. Müller, V. Šverák and B. Yan, Sharp stability results for almost conformai maps in even dimensions, J. Geom. Anal. 9(4) (1999), 671-681
23. S. Müller and M. A. Sychev, Optimal existence theorems for nonhomogeneous differential inclusions, Preprint
24. P. Pedregal, Laminates and microstructure, European J. Appl. Math. 4(2) (1993), 121-149
25. Y. G. Reshetnyak, Space Mappings with Bounded Distortion, Transl. Math. Mono., Amer. Math. Soc., Vol. 73, 1989
26. S. Rickman, Quasiregular Mappings, Springer-Verlag, Berlin, 1993
27. R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, 1972
28. 1,p-stability of the conformal set in higher dimensions, Ann. Inst. H. Poincaré, Analyse Non Linéaire 13(6) (1996), 691-705
29. B. Yan, On rank-one convex and polyconvex conformal energy functions with slow growth, Proc. Roy. Soc. Edinburgh 127A (1997), 651-663
30. B. Yan, Linear boundary values of weakly quasiregular mappings, C. R. Acad. Sci. Paris Ser. I Math. 331 (2000), 379-384
31. B. Yan and Z. Zhou, Stability of weakly almost conformal mappings, Proc. Amer. Math. Soc. 126 (1998), 481-189
32. p-mean coercivity, regularity and relaxation in the calculus of variations, Nonlinear Anal., to appear
33. K. Zhang, On various semiconvex hulls in the calculus of variations, Calc. Var. Partial Differential Equations 6 (1998), 143-160