S k -valued maps minimizing the L p norm of the gradient with free discontinuities
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 3, pp. 321-352.
@article{ASNSP_1991_4_18_3_321_0,
     author = {Carriero, M. and Leaci, A.},
     title = {$S^k$-valued maps minimizing the $L^p$ norm of the gradient with free discontinuities},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {321--352},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 18},
     number = {3},
     year = {1991},
     mrnumber = {1145314},
     zbl = {0753.49018},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1991_4_18_3_321_0/}
}
TY  - JOUR
AU  - Carriero, M.
AU  - Leaci, A.
TI  - $S^k$-valued maps minimizing the $L^p$ norm of the gradient with free discontinuities
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1991
SP  - 321
EP  - 352
VL  - 18
IS  - 3
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1991_4_18_3_321_0/
LA  - en
ID  - ASNSP_1991_4_18_3_321_0
ER  - 
%0 Journal Article
%A Carriero, M.
%A Leaci, A.
%T $S^k$-valued maps minimizing the $L^p$ norm of the gradient with free discontinuities
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1991
%P 321-352
%V 18
%N 3
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1991_4_18_3_321_0/
%G en
%F ASNSP_1991_4_18_3_321_0
Carriero, M.; Leaci, A. $S^k$-valued maps minimizing the $L^p$ norm of the gradient with free discontinuities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 3, pp. 321-352. http://www.numdam.org/item/ASNSP_1991_4_18_3_321_0/

[1] E. Acerbi - N. Fusco, Regularity for minimizers of non-quadratic functionals: the case 1 <p<2, J. Math. Anal. Appl., 140 (1989), 115-135. | MR | Zbl

[2] F.J. Almgrenjr. - E.H. Lieb, Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds, Ann. of Math., 128 (1988), 483-530. | MR | Zbl

[3] L. Ambrosio, A compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. Ital., 3-B (1989), 857-881. | MR | Zbl

[4] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal., 111 (1990), 291-322. | MR | Zbl

[5] L. Ambrosio - G. Dal Maso, The chain rule for the distributional derivatives, Proc. Amer. Math. Soc., to appear. | MR | Zbl

[6] L. Ambrosio - V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via r-convergence, Comm. Pure Appl. Math., 43 (1990), 999-1036. | MR | Zbl

[7] F. Bethuel - H. Brézis - J.M. Coron, Relaxed energies for harmonic maps, Preprint 1989. | MR | Zbl

[8] H. Brézis - J.M. Coron - E.H. Lieb, Harmonic Maps with Defects, Comm. Math. Phys., 107 (1986), 679-705. | MR | Zbl

[9] M. Carriero - A. Leaci, Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Anal. TMA, 15 (1990), 661-677. | MR | Zbl

[10] S. Chandrasekhar, Liquid Crystals. Cambridge University Press, Cambridge, 1977.

[11] E. De Giorgi, Free Discontinuity Problems in Calculus of Variations, Proc. Int. Meeting in J.L. Lions's honour, Paris, June 6-10, 1988, to appear. | Zbl

[12] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del Calcolo delle Variazioni, Atti Accad. Naz. Lincei, 82 (1988), 199-210. | Zbl

[13) E. De Giorgi - M. Carriero - A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal., 108 (1989), 195-218. | MR | Zbl

[14] J. Eells - L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc., 20 (1988), 385-524. | MR | Zbl

[15] J.L. Ericksen, Equilibrium theory of liquid crystals, Adv. Liq. Cryst., Vol. 2, G.H. Brown Ed., Academic Press, New York, 1976, 233-299.

[16] H. Federer, Geometric Measure Theory, Springer Verlag, Berlin, 1969. | MR | Zbl

[17] M. Giaquinta - E. Giusti, The singular set of the minima of certain quadratic functionals, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 11 (1984), 45-55. | Numdam | MR | Zbl

[18] M. Giaquinta - G. Modica, Remarks on the regularity of the minimizers of certain degenerate functionals, Manuscripta Math., 57 (1986), 55-100. | MR | Zbl

[19] M. Giaquinta - G. Modica - J. Sou, Cartesian currents and variational problems for mappings into spheres, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 16 (1989), 393-485. | Numdam | MR | Zbl

[20] M. Giaquinta - G. Modica - J. SOUčEK, The Dirichlet energy of mappings with values into the sphere, Manuscripta Math., 65 (1989), 489-507. | MR | Zbl

[21] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser Verlag, Boston, 1984. | MR | Zbl

[22] R. Hardt - D. Kinderlehrer - F.-H. Lin, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., 105 (1986), 547-570. | MR | Zbl

[23] R. Hardt - F.-H. Lin, Mappings minimizing the LP norm of the gradient, Comm. Pure Appl. Math., 40 (1987), 555-588. | MR | Zbl

[24] R. Hardt - F.-H. Lin, A remark on H1 mappings, Manuscripta Math., 56 (1986), 1-10. | MR | Zbl

[25] U. Massari - M. Miranda, Minimal Surfaces of Codimension One, North-Holland, Amsterdam, 1984. | MR | Zbl

[26] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer Verlag, New York, 1966. | MR | Zbl

[27] R. Schoen - K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom., 18 (1982), 307-335. | MR | Zbl

[28] R. Schoen - K. Uhlenbeck, Boundary regularity and the Dirichlet problem of harmonic maps, J. Differential Geom., 18 (1983), 253-268. | MR | Zbl

[29] P. Tolksdorff, Everywhere regularity for some quasilinear systems with a lack of ellipticity, Ann. Mat. Pura Appl., 134 (1983), 241-266. | MR | Zbl

[30] E. Virga, Drops of nematic liquid crystals, Arch. Rational Mech. Anal., 107 (1989), 371-390. | MR | Zbl