S k -valued maps minimizing the L p norm of the gradient with free discontinuities

M. Carriero; A. Leaci

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)

  • Volume: 18, Issue: 3, page 321-352
  • ISSN: 0391-173X

How to cite

top

Carriero, M., and 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 18.3 (1991): 321-352. <http://eudml.org/doc/84104>.

@article{Carriero1991,
author = {Carriero, M., Leaci, A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {BV functions; harmonic maps; existence; partial regularity; free discontinuity problem},
language = {eng},
number = {3},
pages = {321-352},
publisher = {Scuola normale superiore},
title = {$S^k$-valued maps minimizing the $L^p$ norm of the gradient with free discontinuities},
url = {http://eudml.org/doc/84104},
volume = {18},
year = {1991},
}

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
PB - Scuola normale superiore
VL - 18
IS - 3
SP - 321
EP - 352
LA - eng
KW - BV functions; harmonic maps; existence; partial regularity; free discontinuity problem
UR - http://eudml.org/doc/84104
ER -

References

top
  1. [1] E. Acerbi - N. Fusco, Regularity for minimizers of non-quadratic functionals: the case 1 &lt;p&lt;2, J. Math. Anal. Appl., 140 (1989), 115-135. Zbl0686.49004MR997847
  2. [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. Zbl0673.58013MR970609
  3. [3] L. Ambrosio, A compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. Ital., 3-B (1989), 857-881. Zbl0767.49001MR1032614
  4. [4] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal., 111 (1990), 291-322. Zbl0711.49064MR1068374
  5. [5] L. Ambrosio - G. Dal Maso, The chain rule for the distributional derivatives, Proc. Amer. Math. Soc., to appear. Zbl0685.49027MR969514
  6. [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. Zbl0722.49020MR1075076
  7. [7] F. Bethuel - H. Brézis - J.M. Coron, Relaxed energies for harmonic maps, Preprint 1989. Zbl0793.58011MR1205144
  8. [8] H. Brézis - J.M. Coron - E.H. Lieb, Harmonic Maps with Defects, Comm. Math. Phys., 107 (1986), 679-705. Zbl0608.58016MR868739
  9. [9] M. Carriero - A. Leaci, Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Anal. TMA, 15 (1990), 661-677. Zbl0713.49003MR1073957
  10. [10] S. Chandrasekhar, Liquid Crystals. Cambridge University Press, Cambridge, 1977. 
  11. [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. Zbl0758.49002
  12. [12] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del Calcolo delle Variazioni, Atti Accad. Naz. Lincei, 82 (1988), 199-210. Zbl0715.49014
  13. [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. Zbl0682.49002MR1012174
  14. [14] J. Eells - L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc., 20 (1988), 385-524. Zbl0669.58009MR956352
  15. [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. [16] H. Federer, Geometric Measure Theory, Springer Verlag, Berlin, 1969. Zbl0176.00801MR257325
  17. [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. Zbl0543.49018MR752579
  18. [18] M. Giaquinta - G. Modica, Remarks on the regularity of the minimizers of certain degenerate functionals, Manuscripta Math., 57 (1986), 55-100. Zbl0607.49003MR866406
  19. [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. Zbl0713.49014MR1050333
  20. [20] M. Giaquinta - G. Modica - J. SOUčEK, The Dirichlet energy of mappings with values into the sphere, Manuscripta Math., 65 (1989), 489-507. Zbl0678.49006MR1019705
  21. [21] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser Verlag, Boston, 1984. Zbl0545.49018MR775682
  22. [22] R. Hardt - D. Kinderlehrer - F.-H. Lin, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., 105 (1986), 547-570. Zbl0611.35077MR852090
  23. [23] R. Hardt - F.-H. Lin, Mappings minimizing the LP norm of the gradient, Comm. Pure Appl. Math., 40 (1987), 555-588. Zbl0646.49007MR896767
  24. [24] R. Hardt - F.-H. Lin, A remark on H1 mappings, Manuscripta Math., 56 (1986), 1-10. Zbl0618.58015MR846982
  25. [25] U. Massari - M. Miranda, Minimal Surfaces of Codimension One, North-Holland, Amsterdam, 1984. Zbl0565.49030MR795963
  26. [26] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer Verlag, New York, 1966. Zbl0142.38701MR202511
  27. [27] R. Schoen - K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom., 18 (1982), 307-335. Zbl0521.58021MR664498
  28. [28] R. Schoen - K. Uhlenbeck, Boundary regularity and the Dirichlet problem of harmonic maps, J. Differential Geom., 18 (1983), 253-268. Zbl0547.58020MR710054
  29. [29] P. Tolksdorff, Everywhere regularity for some quasilinear systems with a lack of ellipticity, Ann. Mat. Pura Appl., 134 (1983), 241-266. Zbl0538.35034MR736742
  30. [30] E. Virga, Drops of nematic liquid crystals, Arch. Rational Mech. Anal., 107 (1989), 371-390. Zbl0688.76074MR1004716

Citations in EuDML Documents

top
  1. Luigi Ambrosio, Diego Pallara, Partial regularity of free discontinuity sets, I
  2. Michele Carriero, Antonio Leaci, Franco Tomarelli, Strong minimizers of Blake & Zisserman functional
  3. Irene Fonseca, Nicola Fusco, Regularity results for anisotropic image segmentation models
  4. Guy David, Stephen Semmes, Uniform rectifiability and singular sets
  5. Jean-Michel Morel, The Mumford-Shah conjecture in image processing
  6. Emilio Acerbi, Irene Fonseca, Nicola Fusco, Regularity of minimizers for a class of membrane energies
  7. Guy David, The local regularity of soap films after Jean Taylor

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.