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Local regularity for minimizers of non convex integrals

E. Acerbi; N. Fusco

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 4, page 603-636
  • ISSN: 0391-173X

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Acerbi, E., and Fusco, N.. "Local regularity for minimizers of non convex integrals." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.4 (1989): 603-636. <http://eudml.org/doc/84064>.

@article{Acerbi1989,
author = {Acerbi, E., Fusco, N.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {minimizers; nonconvex integrals; functional; sequentially lower semicontinuous; existence; regularity; strictly quasiconvex functionals; nonlinear elasticity},
language = {eng},
number = {4},
pages = {603-636},
publisher = {Scuola normale superiore},
title = {Local regularity for minimizers of non convex integrals},
url = {http://eudml.org/doc/84064},
volume = {16},
year = {1989},
}

TY - JOUR
AU - Acerbi, E.
AU - Fusco, N.
TI - Local regularity for minimizers of non convex integrals
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 4
SP - 603
EP - 636
LA - eng
KW - minimizers; nonconvex integrals; functional; sequentially lower semicontinuous; existence; regularity; strictly quasiconvex functionals; nonlinear elasticity
UR - http://eudml.org/doc/84064
ER -

References

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  1. [1] E. Acerbi - N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal.86 (1984), 125-145. Zbl0565.49010MR751305
  2. [2] E. Acerbi - N. Fusco, A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal.99 (1987), 261-281. Zbl0627.49007MR888453
  3. [3] G. Anzellotti - M. Giaquinta, Convex functionals and partial regularity. Arch. Rational Mech. Anal.102 (1988), 243-272. Zbl0658.49005MR944548
  4. [4] I. Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc.1 (1979), 443-474. Zbl0441.49011MR526967
  5. [5] L.C. Evans, Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal.95 (1986), 227-252. Zbl0627.49006MR853966
  6. [6] L.C. Evans - R.F. Gariepy, Blow-up, compactness and partial regularity in the calculus of variations. Indiana Univ. Math. J.36 (1987), 361-371. Zbl0626.49007MR891780
  7. [7] N. Fusco - J. Hutchinson, C1.α partial regularity of functions minimising quasiconvex integrals. Manuscripta Math.54 (1985), 121-143. Zbl0587.49005
  8. [8] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Ann. of Math. Studies105, Princeton University Press, Princeton, 1983. Zbl0516.49003MR717034
  9. [9] M. Giaquinta, Quasiconvexity, growth conditions, and partial regularity. Partial differential equations and calculus of variations, 211-237, Lecture Notes in Math., 1357, Springer, Berlin-New York, 1988. Zbl0658.49006MR976237
  10. [10] M. Giaquinta - E. Giusti, On the regularity of minima of variational integrals. Acta Math.148 (1982), 31-46. Zbl0494.49031MR666107
  11. [11] M. Giaquinta - G. Modica, Partial regularity of minimizers of quasiconvex integrals. Ann. Inst. H. Poincaré, Analyse non linéaire3 (1986), 185-208. Zbl0594.49004MR847306
  12. [12] M.C. Hong, Existence and partial regularity in the calculus of variations. Ann. Mat. Pura Appl.149 (1987), 311-328. Zbl0648.49008MR932791
  13. [13] P. Marcellini - C. Sbordone, On the existence of minima of multiple integrals in the calculus of variations. J. Math. Pures Appl. 62 (1983), 1-9. Zbl0516.49011MR700045
  14. [14] N.G. Meyers, Quasi-convexity and lower semicontinuity of multiple variational integrals of any order. Trans. Amer. Math. Soc.119 (1965), 1-28. Zbl0166.38501MR188838
  15. [15] C.B. MorreyJr., Quasi-convexity and the semicontinuity of multiple integrals. Pacific J. Math.2 (1952), 25-53. Zbl0046.10803MR54865
  16. [16] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems. Acta Math.138 (1977), 219-240. Zbl0372.35030MR474389

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