Generalised Twists, $\mathrm{SO}\left(n\right)$, and the $p$-Energy Over a Space of Measure Preserving Maps
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 5, p. 1897-1924
@article{AIHPC_2009__26_5_1897_0,
author = {Shahrokhi-Dehkordi, M. S. and Taheri, A.},
title = {Generalised Twists, $\mathrm {SO}\left(n\right)$, and the $p$-Energy Over a Space of Measure Preserving Maps},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {26},
number = {5},
year = {2009},
pages = {1897-1924},
doi = {10.1016/j.anihpc.2009.03.003},
zbl = {1172.74021},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2009__26_5_1897_0}
}

Shahrokhi-Dehkordi, M. S.; Taheri, A. Generalised Twists, $\mathrm {SO}\left(n\right)$, and the $p$-Energy Over a Space of Measure Preserving Maps. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 5, pp. 1897-1924. doi : 10.1016/j.anihpc.2009.03.003. http://www.numdam.org/item/AIHPC_2009__26_5_1897_0/

[1] Ball J. M., Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Ration. Mech. Anal. 63 (1977) 337-403. | MR 475169 | Zbl 0368.73040

[2] Ball J. M., Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Philos. Trans. Roy. Soc. Ser. A 306 (1982) 557-611. | MR 703623 | Zbl 0513.73020

[3] Bauman P., Owen N. C., Phillips D., Maximum Principles and a Priori Estimates for an Incompressible Material in Nonlinear Elasticity, Comm. Partial Differential Equations 17 (1992) 1185-1212. | MR 1179283 | Zbl 0777.35014

[4] Bredon G., Topology and Geometry, Graduate Texts in Mathematics, vol. 139, Springer, 1993. | MR 1224675 | Zbl 0791.55001

[5] Cesari L., Optimization-Theory and Application, Applications of Mathematics, vol. 17, Springer, 1983. | MR 688142 | Zbl 0506.49001

[6] Evans L. C., Gariepy R. F., On the Partial Regularity of Energy-Minimizing, Area Preserving Maps, Calc. Var. 63 (1999) 357-372. | MR 1731471 | Zbl 0954.49024

[7] Kato T., Perturbation Theory for Linear Operators, Graduate Texts in Mathematics, vol. 132, Springer-Verlag, 1980. | Zbl 0435.47001

[8] Knops R. J., Stuart C. A., Quasiconvexity and Uniqueness of Equilibrium Solutions in Nonlinear Elasticity, Arch. Ration. Mech. Anal. 86 (3) (1984) 233-249. | MR 751508 | Zbl 0589.73017

[9] Post K., Sivaloganathan J., On Homotopy Conditions and the Existence of Multiple Equilibria in Finite Elasticity, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997) 595-614. | MR 1453283 | Zbl 0878.73025

[10] Shahrokhi-Dehkordi M. S., Taheri A., Generalised Twists, Stationary Loops and the Dirichlet Energy on a Space of Measure Preserving Maps, Calc. Var. Partial Differential Equations 35 (2) (2009) 191-213. | MR 2481822 | Zbl 1160.49040

[11] M.S. Shahrokhi-Dehkordi, A. Taheri, in preparation.

[12] Sivaloganathan J., Uniqueness of Regular and Singular Equilibria for Spherical Symmetric Problems of Nonlinear Elasticity, Arch. Ration. Mech. Anal. 96 (3) (1986) 97-136. | MR 853969 | Zbl 0628.73018

[13] Taheri A., Local Minimizers and Quasiconvexity - the Impact of Topology, Arch. Ration. Mech. Anal. 176 (3) (2005) 363-414. | MR 2185663 | Zbl 1073.49007

[14] Taheri A., Minimizing the Dirichlet Energy on a Space of Measure Preserving Maps, Topol. Methods Nonlinear Anal. 33 (1) (2009) 179-204. | MR 2524492 | Zbl 1172.49005

[15] A. Taheri, On a topological degree on the space of self-maps of annuli, submitted for publication.