Partial regularity for minimizers of variational integrals with discontinuous integrands

Christoph Hamburger

Annales de l'I.H.P. Analyse non linéaire (1996)

• Volume: 13, Issue: 3, page 255-282
• ISSN: 0294-1449

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Hamburger, Christoph. "Partial regularity for minimizers of variational integrals with discontinuous integrands." Annales de l'I.H.P. Analyse non linéaire 13.3 (1996): 255-282. <http://eudml.org/doc/78382>.

@article{Hamburger1996,
author = {Hamburger, Christoph},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {quasiconvexity; discontinuous integrand; strict convexity},
language = {eng},
number = {3},
pages = {255-282},
publisher = {Gauthier-Villars},
title = {Partial regularity for minimizers of variational integrals with discontinuous integrands},
url = {http://eudml.org/doc/78382},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Hamburger, Christoph
TI - Partial regularity for minimizers of variational integrals with discontinuous integrands
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 3
SP - 255
EP - 282
LA - eng
KW - quasiconvexity; discontinuous integrand; strict convexity
UR - http://eudml.org/doc/78382
ER -

References

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1. [A-F] E. Acerbi and N. Fusco, A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal., Vol. 99, 1987, pp. 261-281. Zbl0627.49007MR888453
2. [E1] L.C. Evans, Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal., Vol. 95, 1986, pp. 227-252. Zbl0627.49006MR853966
3. [E2] L.C. Evans, Weak convergence methods for nonlinear partial differential equations. Regional conference series in mathematics, Vol. 74, AMS, Providence, 1990. Zbl0698.35004MR1034481
4. [E-G1] L.C. Evans and R.F. Gariepy, Blow-up, compactness and partial regularity in the calculus of variations. Indiana Univ. Math. J., Vol. 36, 1987, pp. 361-371. Zbl0626.49007MR891780
5. [E-G2] L.C. Evans and R.F. Gariepy, Some remarks concerning quasiconvexity and strong convergence. Proc. Royal Soc. Edinburgh, Vol. 106A, 1987, pp. 53-61. Zbl0628.49011MR899940
6. [F-H] N. Fusco and J. Hutchinson, C1,α partial regularity of functions minimising quasiconvex integrals. Manuscripta math., Vol. 54, 1985, pp. 121-143. Zbl0587.49005MR808684
7. [G1] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton Univ. Press, Princeton, 1983. Zbl0516.49003MR717034
8. [G2] M. Giaquinta, The problem of the regularity of minimizers. International congress of mathematicians, Berkeley, 1986. Zbl0667.49029MR934310
9. [G3] M. Giaquinta, Quasiconvexity, growth conditions and partial regularity. In: S. HILDEBRANDT and R. LEIS (Eds.) Partial differential equations and calculus of variations. Lecture notes in mathematics, Vol. 1357, Springer, Berlin, 1988. Zbl0658.49006MR976237
10. [G-G1] M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals. Acta Math., Vol. 148, 1982, pp. 31-46. Zbl0494.49031MR666107
11. [G-G2] M. Giaquinta and E. Giusti, Differentiability of minima of nondifferentiable functionals. Inv. Math., Vol. 72, 1983, pp. 285-298. Zbl0513.49003MR700772
12. [G-M] M. Giaquinta and G. Modica, Partial regularity of minimizers of quasiconvex integrals. Ann. Inst. H. Poincaré, Analyse non linéaire, Vol 3, 1986, pp. 185-208. Zbl0594.49004MR847306
13. [H] C. Hamburger, An elementary partial regularity proof for solutions of nonlinear elliptic systems. SFB256, Bonn, Preprint 353, 1994. MR1014470
14. [Ho] M.C. Hong, Existence and partial regularity in the calculus of variations. Ann. Mat. Pura Appl., Vol. 149, 1987, pp. 311-328. Zbl0648.49008MR932791
15. [R] W. Rudin, Real and complex analysis. McGraw-Hill, New York, 1987. Zbl0925.00005MR924157

Citations in EuDML Documents

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1. Christoph Hamburger, Partial Boundary Regularity of Solutions of Nonlinear Superelliptic Systems
2. Christoph Hamburger, Optimal partial regularity of minimizers of quasiconvex variational integrals
3. Giuseppe Mingione, Regularity of minima: an invitation to the Dark Side of the Calculus of Variations

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