Singular minimisers in the calculus of variations : a degenerate form of cavitation
Annales de l'I.H.P. Analyse non linéaire (1992)
- Volume: 9, Issue: 6, page 657-681
- ISSN: 0294-1449
Access Full Article
topHow to cite
topSivaloganathan, J.. "Singular minimisers in the calculus of variations : a degenerate form of cavitation." Annales de l'I.H.P. Analyse non linéaire 9.6 (1992): 657-681. <http://eudml.org/doc/78294>.
@article{Sivaloganathan1992,
author = {Sivaloganathan, J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular minimizers; cavitation; elastic body; energy integral; radial maps; existence of minimizers; smooth variations; stability},
language = {eng},
number = {6},
pages = {657-681},
publisher = {Gauthier-Villars},
title = {Singular minimisers in the calculus of variations : a degenerate form of cavitation},
url = {http://eudml.org/doc/78294},
volume = {9},
year = {1992},
}
TY - JOUR
AU - Sivaloganathan, J.
TI - Singular minimisers in the calculus of variations : a degenerate form of cavitation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 6
SP - 657
EP - 681
LA - eng
KW - singular minimizers; cavitation; elastic body; energy integral; radial maps; existence of minimizers; smooth variations; stability
UR - http://eudml.org/doc/78294
ER -
References
top- [1] J.M. Ball, Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Phil. Trans. Roy. Soc. London., Vol. A306, 1982, pp. 557-611. Zbl0513.73020MR703623
- [2] J.M. Ball and F. Murat, W1,p-Quasiconvexity and Variational Problems for Multiple Integrals, J. Funct. Anal., Vol. 58, 1984, pp.225-253. Zbl0549.46019MR759098
- [3] J.M. Ball, J.C. Currie and P.J. Olver, Null Lagrangians, Weak Continuity and Variational Problems of Arbitrary Order, J. Funct. Anal., Vol. 41, 1981, pp. 135-174. Zbl0459.35020MR615159
- [4] H. Brezis, J. Coron and E. Lieb, Harmonic Maps with Defects, Comm. Math. Phys., Vol. 107, 1986, pp. 649-705. Zbl0608.58016MR868739
- [5] H. Brezis, Sk-valued maps with singularities, Montecatini Lecture Notes, Springer, 1988. Zbl0684.49015MR994017
- [6] D.G. Edelen, The null set of the Euler-Lagrange Operator, Arch. Ration. Mech. Anal., Vol. 11, 1962, pp. 117-121. Zbl0125.33002MR150623
- [7] L.C. Evans, Quasiconvexity and Partial Regularity in the Calculus of Variations, Arch. Ration. Mech. Anal., Vol. 95, 1986, pp. 227-252. Zbl0627.49006MR853966
- [8] N. Fusco and J. Hutchinson, Partial Regularity of Functions Minimising Quasiconvex Integrals, Manuscripta Math., Vol. 54, 1985, pp. 121-143. Zbl0587.49005MR808684
- [9] A.N. Gent and P.B. Lindley, Internal Rupture of Bonded Rubber Cylinders in Tension, Proc. Roy. Soc. London, Vol. A249, 1958, pp. 195-205.
- [10] R. Hardt, D. Kinderlehrer and F.H. Lin, Existence and Partial Regularity of Static Liquid Crystal Configurations, Commun. Math. Phys., Vol. 105, 1986, pp. 541-570. Zbl0611.35077MR852090
- [11] F. Helein, Applications harmoniques et applications minimisantes entre variétés Riemanniennes, Thèse de Doctorat, École Polytechnique, 1989.
- [12] C.O. Horgan and R. Abeyaratne, A Bifurcation Problem for a Compressible Nonlinearly Elastic Medium: Growth of a Microvoid, J. Elasticity, Vol. 16, 1986, pp. 189-200. Zbl0585.73017MR849671
- [13] R.D. James and S.J. Spector, The Formation of Filamentary Voids in Solids, J. Mech. Phys. Sol., Vol. 39, 1991, pp. 783-813. Zbl0761.73020MR1120242
- [14] F.H. Lin, Une remarque sur l'application x/|x|, C.R. Acad. Sci. Paris, T. 305, Series I, 1987, pp. 529-531. Zbl0652.58022
- [15] S. Muller, Higher Integrability of Determinants and Weak Convergence in L1, J. reine angew. Math., Vol. 412, 1990, pp. 20-34. Zbl0713.49004MR1078998
- [16] P.J. Olver and J. Sivaloganathan, The Structure of Null Lagrangians, Nonlinearity, Vol. 1, 1988, pp. 389-398. Zbl0662.49016MR937008
- [17] R. Osserman, The Isoperimetric Inequality, Bull. Amer. Math. Soc., Vol. 84, 1978, pp. 1182-1238. Zbl0411.52006MR500557
- [18] K.A. Pericak-Spector and S.J. Spector, Nonuniqueness for a Hyperbolic System: Cavitation in Nonlinear Elastodynamics, Arch. Ration. Mech. Anal., Vol. 101, 1988, pp. 293-317. Zbl0651.73005MR930330
- [19] P. Podio-Guidugli, G. Vergara Caffarelli and E.G. Virga, Discontinuous Energy Minimisers in Nonlinear Elastostatics: an Example of J. Ball Revisited, J. Elasticity, Vol. 16, 1986, pp. 75-96. Zbl0575.73021MR835366
- [20] Polya and Szego, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, 1951. Zbl0044.38301MR43486
- [21] J. Sivaloganathan, Uniqueness of Regular and Singular Equilibria for Spherically Symmetric Problems of Nonlinear Elasticity, Arch. Ration. Mech. Anal., Vol. 96, 1986, pp. 97-136. Zbl0628.73018MR853969
- [22] J. Sivaloganathan, A Field Theory Approach to Stability of Equilibria in Radial Elasticity, Math. Proc. Camb. Phil. Soc., Vol. 99, 1986, pp. 589-604. Zbl0612.73013MR830370
- [23] J. Sivaloganathan, The Generalised Hamilton-Jacobi Inequality and the Stability of Equilibria in Nonlinear Elasticity, Arch. Ration. Mech. Anal., Vol. 107, No. 4, 1989, pp. 347-369. Zbl0709.73014MR1004715
- [24] J. Sivaloganathan, in preparation.
- [25] S. Spector, Linear Deformations as Minimisers of the Energy, preprint.
- [26] C.A. Stuart, Radially Symmetric Cavitation for Hyperelastic Materials, Ann. Inst. Henri Poincaré: Analyse non linéaire, Vol. 2, 1985, pp. 33-66. Zbl0588.73021MR781591
- [27] C.A. Stuart, Estimating the Critical Radius for Radially Symmetric Cavitation, preprint E.P.F.L.Lausanne, 1991. Zbl0790.73016MR1218367
- [28] F. Meynard, Cavitation dans un milieu hyperélastique, Thèse de Doctorat, École Polytechnique Fédérale de Lausanne, 1990.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.