@article{ASNSP_1989_4_16_3_393_0, author = {Giaquinta, M. and Modica, G. and Sou\v{c}ek, J.}, title = {Cartesian currents and variational problems for mappings into spheres}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {393--485}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 16}, number = {3}, year = {1989}, mrnumber = {1050333}, zbl = {0713.49014}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1989_4_16_3_393_0/} }
TY - JOUR AU - Giaquinta, M. AU - Modica, G. AU - Souček, J. TI - Cartesian currents and variational problems for mappings into spheres JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1989 SP - 393 EP - 485 VL - 16 IS - 3 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1989_4_16_3_393_0/ LA - en ID - ASNSP_1989_4_16_3_393_0 ER -
%0 Journal Article %A Giaquinta, M. %A Modica, G. %A Souček, J. %T Cartesian currents and variational problems for mappings into spheres %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1989 %P 393-485 %V 16 %N 3 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1989_4_16_3_393_0/ %G en %F ASNSP_1989_4_16_3_393_0
Giaquinta, M.; Modica, G.; Souček, J. Cartesian currents and variational problems for mappings into spheres. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 16 (1989) no. 3, pp. 393-485. http://archive.numdam.org/item/ASNSP_1989_4_16_3_393_0/
[1] Co-area, Liquid crystals, and minimal surfaces, In DDT - a selection of Papers, Springer-Verlag, 1987. | MR
- - ,[2] Singularities of energy minimizing maps from the ball to the sphere: examples, counterexamples, and bounds, Preprint.
- ,[3] Functionals with linear growth defined on vector valued BV functions, preprint. | MR
- - ,[4] Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal. 63 (1977). | MR | Zbl
,[5] Global invertibility of Sobolev functions and the interpenetration of matter, Proc. Roy. Soc. Edinburgh A 88 (1981) 315-328. | MR | Zbl
,[6] Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Philos. Trans. Roy. Soc. A 306 (1982) 577-611. | MR | Zbl
,[7] W1.p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225-253. | MR | Zbl
- ,[8] A characterization of maps in H1 (B3,S 2) which can be approximated by smooth maps, preprint.
,[9] Approximation dans des espaces de Sobolev entre deux variété et groupes d' homotopie, preprint. | MR
,[10] Density of smooth functions between two manifolds in Sobolev spaces, preprint. | MR
- ,[11] Elliptic problem image segmentation and their relation to fracture theory, preprint.
- ,[12] Differential forms in Algebraic Topology, Springer-Verlag, New York, 1982. | MR | Zbl
- ,[13] Metastable harmonic maps, In "Metastability and incompletely posed problems" Eds. S. Antman, J.L. Ericksen, D. Kinderlehrer, J. Müller, Springer-Verlag 1987. | MR
,[14] Sk-valued maps with singularities, In "Topics in Calculus of Variations" Ed. M. Giaquinta, Lecture Notes in Math. n.1365, Springer-Verlag 1989. | MR | Zbl
,[15] Large solutions for harmonic maps in two dimensions, Commun. Math. Phys. 92 (1983) 203-215. | MR | Zbl
- ,[16] Harmonic maps with defects, Comm. Math. Phys. 107 (1986), 649-705. | MR | Zbl
- - ,[17] Convex bodies and convexity on Grassmann cones, Part I to IV Math. Ann. 151 (1963) 1-41. | MR | Zbl
- ,[18] Unilateral problems in nonlinear, three-dimensional elasticity, Arch. Rat. Mech. Anal. 97 (1987) 171-188.
- ,[19] Remarques sur les notions de polyconvexité, quasi-convexité et convexité de rang 1. J. Math. pures et Appl. 64 (1985) 403-438. | MR | Zbl
,[20] Integral representation on BV(Ω) of r-limits of variational integrals. Manuscripta Math. 30 (1980) 387-416. | Zbl
,[21] Un nuovo tipo di funzionale del calcolo delle variazioni, preprint.
- ,[22] Existence theorem for a minimum problem with free discontinuity set, preprint.
- - ,[23] A report on harmonic maps, Bull. London Math. Soc. 10 (1978) 1-69. | MR | Zbl
- ,[24] Selected topics in harmonic maps, Amer. Mat. Soc. Regional Conf. Series in Math. 50, 1983. | MR | Zbl
- ,[25] Another report on harmonic maps, Bull. London Math. Soc. 20 (1988) 385-524. | MR | Zbl
- ,[26] Restrictions on harmonic maps of surfaces, Topology 15 (1976) 263-266. | MR | Zbl
- ,[27] Convex analysis and variational problems, North Holland, Amsterdam 1976. | MR | Zbl
- ,[28] Theory and applications of liquid crystals, IMA Series vol 5, Springer-Verlag 1987. | MR | Zbl
- ,[29] A direct variational approach to Skyrme's model for meson fields, Comm. Math. Phys. 105 (1986) 571-591. | MR | Zbl
,[30] Geometric measure theory, Springer-Verlag, New York, 1969. | MR | Zbl
,[31] Normal and integral currents, Ann. of Math. 72 (1960) 458-520. | MR | Zbl
- ,[32] The singular set of the minima of certain quadratic functionals, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), 45-55. | Numdam | MR | Zbl
- ,[33] Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity, Archive for Rat. Mech. Anal. 106 (1989) 97-159. Erratum and addendum, to appear in Archive for Rat. Mech. Anal. | MR | Zbl
- - ,[34] Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys. 105 (1986), 547-570. | MR | Zbl
- - ,[35] A remark about the stability of smooth equilibrium configurations of static liquid crystals, Mol. Cryst. Liq, Cryst. 139 (1986) 189-194.
- - ,[36] Stable defects of minimizers of constrained variational principles, Ann. Inst. Henri Poincaré 5 (1988) 207-322. | Numdam | MR | Zbl
- - ,[37] A remark on H1 mappings, Manuscripta Math. 56 (1986) 1010. | MR | Zbl
- ,[38] Seminar on Geometric Measure Theory, Birkhäuser, Boston, 1986. | MR | Zbl
- ,[39] The Dirichlet problem for harmonic maps from a surface with boundary into a 2-sphere with non-constant boundary values, J. Diff. Geom. 19 (1984) 393-401. | MR | Zbl
,[40] Harmonic maps between surfaces, Lecture notes in Math. 1062, Springer-Verlag 1984. | MR | Zbl
,[41] Optimal design and relaxation of variational problems, Comm. Pure Appl. Math. to appear.
- ,[42] Applications harmoniques de surfaces riemanniennes, J.Diff. Geom. 13 (1978) 51-78. | MR | Zbl
,[43] The concentration compactness principle in the calculus of variations. The limit case, part 2, Revista Matematica Iberoamericana 1 (1985) 45-121. | MR | Zbl
,[44] A Lusin type property of Sobolev functions, Indiana Univ. Math. J. 26 (1977) 645-671. | MR | Zbl
,[45] The stored energy of some discontinuous deformations in nonlinear elasticity, In Partial Differential Equations and the Calculus of Variations: Essays in Honor of Ennio De Giorgi, Birkäuser, Boston, 1989, to appear. | MR | Zbl
,[46] Removable singularities of harmonic maps and an application to minimized submanifolds, Indiana Univ. Math. J. 35 (1986) 705-726. | MR | Zbl
,[47] Segmentation of images by variational methods, preprint.
, ,[48] Geometric measure theory, Academic Press, 1988. | MR | Zbl
,[49] Multiple integrals in the calculus of variations, Springer-Verlag, Berlin, 1966. | MR | Zbl
,[50] Weak continuity of determinants and nonlinear elasticity, C.R. Acad. Sci. Paris 307 (1988) 501-576. | MR | Zbl
,[51] Boundary detection by minimizing functionals, Proceedings of the IEEE. Conference on computer vision and pattern recognition, San Francisco, 1985.
, ,[52] Topics in Nonlinear Functionals Analysis, New York University, Lectures Notes, New York (1974). | MR | Zbl
,[53] Almost-everywhere injectivity in nonlinear elasticity, Proc. Roy. Soc. Edinburgh 109A (1988) 79-95. | MR | Zbl
,[54] On the stability of conformal mappings in multidimensional spaces, Siberian Math. J. 8 (1967) 69-85. | Zbl
,[55] Stability theorems for mappings with bounded distorsion, Siberian Math. J. 9 (1968) 499-512. | MR | Zbl
,[56] Weak convergence of completely additive vector functions on a set, Sibirskii Mat. Zhurnal 9 (1968) 1386-1394. | MR | Zbl
,[57] A regularity theory for harmonic maps, J. Diff. Geom. 17 (1982) 307-335. | MR | Zbl
- ,[58] Boundary regularity and miscellaneous results on harmonic maps, J. Diff. Geom. 18 (1983) 253-268. | MR | Zbl
- ,[59] Lectures on Geometric Measure Theory, Proc. of the Centre for Math. Analysis vol. 3 Australian National University, Canberra, 1983. | MR | Zbl
,[60] The Dirichlet problem for harmonic maps from the disc into 2-sphere, preprint. | MR
,[61] Regularity properties of deformations with finite energy, Arch. Rat. Mech. Anal. 98 (1987). | MR | Zbl
,[62] A new proof of the compactness theorem for integral currents, preprint. | MR
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