On the singular set for Lipschitzian critical points of polyconvex functionals

Journal of Mathematical Analysis and Applications

Volumn 336, Issue 1, 2007, Pages 372-398

  Cho, Sungwon ^a   Yan, Xiaodong ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Hausdorff dimension; Partial regularity; Polyconvexity

Indexed keywords

EID: 34547096972     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.02.078     Document Type: Article

References (16)

1. Acerbi E., and Fusco N. Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Anal. 86 (1984) 125-145
2. Evans L.C. Quasiconvexity and partial regularity in the calculus of variations. Arch. Ration. Mech. Anal. 95 (1986) 227-252
3. 1, α partial regularity of functions minimising quasi-convex integrals. Manuscripta Math. 54 (1985) 121-143
4. Fusco N., and Hutchinson J. Partial regularity in problems motivated by nonlinear elasticity. SIAM J. Math. Anal. 72 6 (1991) 1516-1551
5. Fusco N., and Hutchinson J. Partial regularity and everywhere continuity for a model problem from nonlinear elasticity. J. Aust. Math. Soc. Ser. A 57 2 (1994) 158-169
6. Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems (1983), Princeton Univ. Press, Princeton, NJ
7. Giaquinta M., and Modica G. Partial regularity of minimizers of quasi-convex integrals. Ann. Inst. H. Poincaré 3 (1986) 185-208
8. Kristensen J., and Mingione G. The singular set of minima of integral functionals. Arch. Ration. Mech. Anal. 180 3 (2006) 331-398
9. J. Kristensen, G. Mingione, The singular set of Lipschitzian minima of multiple integrals, Arch. Ration. Mech. Anal., in press
10. Kristensen J., and Taheri A. Partial regularity of strong local minimizers in the multi-dimensional calculus of variations. Arch. Ration. Mech. Anal. 170 (2003) 63-89
11. Mattila P. Geometry of Sets and Measures in the Euclidean Spaces (1995), Cambridge Univ. Press
12. Morrey C.B. Multiple Integrals in the Calculus of Variations (1966), Springer-Verlag, New York
13. R. Moser, Vanishing mean oscillation and regularity in the calculus of variations, MPI, preprint, 2001
14. Müller S., and Šverák V. Convex integration for Lipschitz mappings and counterexamples to regularity. Ann. of Math. (2) 157 (2003) 715-742
15. n. Proc. London Math. Soc. (3) 62 (1991) 353-372
16. Székelyhidi Jr. L. The regularity of critical points of polyconvex functionals. Arch. Ration. Mech. Anal. 172 1 (2004) 133-152