Partial regularity of minimizers of quasiconvex integrals

Mariano Giaquinta; Giuseppe Modica

Annales de l'I.H.P. Analyse non linéaire (1986)

  • Volume: 3, Issue: 3, page 185-208
  • ISSN: 0294-1449

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Giaquinta, Mariano, and Modica, Giuseppe. "Partial regularity of minimizers of quasiconvex integrals." Annales de l'I.H.P. Analyse non linéaire 3.3 (1986): 185-208. <http://eudml.org/doc/78111>.

@article{Giaquinta1986,
author = {Giaquinta, Mariano, Modica, Giuseppe},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {quasiconvexity; variational integrals; minimizer},
language = {eng},
number = {3},
pages = {185-208},
publisher = {Gauthier-Villars},
title = {Partial regularity of minimizers of quasiconvex integrals},
url = {http://eudml.org/doc/78111},
volume = {3},
year = {1986},
}

TY - JOUR
AU - Giaquinta, Mariano
AU - Modica, Giuseppe
TI - Partial regularity of minimizers of quasiconvex integrals
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 3
SP - 185
EP - 208
LA - eng
KW - quasiconvexity; variational integrals; minimizer
UR - http://eudml.org/doc/78111
ER -

References

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  2. [2] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal., t. 63, 1977, p. 337-403. Zbl0368.73040MR475169
  3. [3] R.R. Coiffman, C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals. Studia Math., t. 51, 1974, p. 241-250. Zbl0291.44007MR358205
  4. [4] E. DE Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari. Mem. Accad. Sci. Torino, cl. Sci. Fis. Mat. Nat., (3), t. 3, 1957, p. 25-43. Zbl0084.31901MR93649
  5. [5] E. Di Benedetto, T.S. Trudinger, Harnack inequalities for quasi-minima of variational integrals. Ann. Inst. H. Poincaré. Analyse non linéaire. Zbl0565.35012
  6. [6] C.L. Evans, Quasiconvexity and partial regularity in the calculus of variations. Preprint. Zbl0627.49006
  7. [7] F.W. Gehring, The Lp integrability of the partial derivatives of a quasi conformal mapping. Acta Math., t. 130, 1973, p. 265-277. Zbl0258.30021MR402038
  8. [8] M. Giaquinta, Multiple integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Princeton Univ. Press, Princeton, 1983. Zbl0516.49003MR717034
  9. [9] M. Giaquinta, E. Giusti, On the regularity of minima of variational integrals. Acta Math., t. 148, 1982, p. 31-46. Zbl0494.49031MR666107
  10. [10] M. Giaquinta, E. Giusti, Differentiability of minima of non-differentiable functionals. Inventiones Math., t. 72, 1983, p. 285-298. Zbl0513.49003MR700772
  11. [11] M. Giaquinta, E. Giusti, Quasi-minima. Ann. Inst. H. Poincaré, Analyse non linéaire, t. 1, 1984, p. 79-107. Zbl0541.49008MR752579
  12. [12] M. Giaquinta, E. Giusti, Sharp estimates for the derivatives of local minima of variational integrals. Boll. U. M. I. (6), t. 3-A, 1984, p. 239-248. Zbl0543.49019MR753882
  13. [13] M. Giaquinta, P.A. Ivert, Partial regularity for minima of variational integrals. Preprint FIM, ETHZürich, 1984. Zbl0637.49005MR923408
  14. [14] M. Giaquinta, G. Modica, Regularity results for some classes of higher order nonlinear elliptic systems. J. reine u. angew. Math., t. 311-312, 1979, p. 145-169. Zbl0409.35015MR549962
  15. [15] M. Giaquinta, G. Modica, Almost-everywhere regularity results for solutions of nonlinear elliptic systems. Manuscripta math., t. 28, 1979, p. 109-158. Zbl0411.35018MR535699
  16. [16] M. Giaquinta, J. Soucek, Caccioppoli's inequality and Legendre-Hadamard condition. Math. Ann., t. 270, 1985, p. 105-107. Zbl0561.35027MR769613
  17. [17] C.B. Morrey, jr., Quasi convexity and the lower semicontinuity of multiple integrals. Pacific J. Math., t. 2, 1952, p. 25-53. Zbl0046.10803MR54865
  18. [16] C.B. Morrey, jr., Multiple integrals in the Calculus of Variations. Springer Verlag, Heidelberg, 1966. Zbl0142.38701MR202511

Citations in EuDML Documents

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  1. Menita Carozza, Antonia Passarelli di Napoli, Model problems from nonlinear elasticity: partial regularity results
  2. E. Acerbi, N. Fusco, Local regularity for minimizers of non convex integrals
  3. Christoph Hamburger, Partial regularity for minimizers of variational integrals with discontinuous integrands
  4. R. Hardt, D. Kinderlehrer, Fang-Hua Lin, Stable defects of minimizers of constrained variational principles
  5. Menita Carozza, Irene Fonseca, Antonia Passarelli di Napoli, Regularity results for an optimal design problem with a volume constraint
  6. Manfred Kronz, Partial regularity results for minimizers of quasiconvex functionals of higher order
  7. Mikil Foss, Giuseppe Mingione, Partial continuity for elliptic problems
  8. Paolo Marcellini, On the definition and the lower semicontinuity of certain quasiconvex integrals
  9. Manfred Kronz, Quasimonotone systems of higher order
  10. Christoph Hamburger, Optimal partial regularity of minimizers of quasiconvex variational integrals

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