Partial regularity results for minimizers of quasiconvex functionals of higher order
Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 1, p. 81-112
@article{AIHPC_2002__19_1_81_0,
     author = {Kronz, Manfred},
     title = {Partial regularity results for minimizers of quasiconvex functionals of higher order},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {19},
     number = {1},
     year = {2002},
     pages = {81-112},
     zbl = {1010.49023},
     mrnumber = {1902546},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_1_81_0}
}
Kronz, Manfred. Partial regularity results for minimizers of quasiconvex functionals of higher order. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 1, pp. 81-112. http://www.numdam.org/item/AIHPC_2002__19_1_81_0/

[1] Acerbi E., Fusco N., Semicontinuity of problems in the calculus of variations, Arch. Rat. Mech. Anal. 86 (1984) 125-145. | MR 751305 | Zbl 0565.49010

[2] Ball J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal. 63 (1977) 337-403. | MR 475169 | Zbl 0368.73040

[3] Campanato S., Proprietà di una famiglia di spazi funzionali, Ann. Scoula Norm. Sup. Pisa 18 (1964) 137-160. | Numdam | MR 167862 | Zbl 0133.06801

[4] Campanato S., Teoremi di interpolazione per tranformazioni che applicano Lp in Ch,α, Ann. Scoula Norm. Sup. Pisa 18 (1964) 345-360. | Numdam | Zbl 0135.35102

[5] Campanato S., Equazioni ellitichi del IIe ordine e spazi L2,λ, Ann. Mat. Pura Appl. 69 (1965) 321-381. | Zbl 0145.36603

[6] Campanato S., Alcune osservazioni relative alle soluzioni di equazioni ellittiche di ordine 2m, in: Atti Convegno Equaz. Der. Parz., Bologna, 1967, pp. 17-25. | MR 264207

[7] Dacorogna B., Direct Methods in the Calculus of Variations, Springer, Berlin, 1989. | MR 990890 | Zbl 0703.49001

[8] Duzaar F., Steffen K., Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, preprint. | MR 1900994

[9] Evans L.C., Quasiconvexitity and partial regularity in the calculus of variations, Arch. Rat. Mech. Anal. 95 (1986) 227-252. | MR 853966 | Zbl 0627.49006

[10] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. | MR 1158660 | Zbl 0804.28001

[11] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, 1983. | MR 717034 | Zbl 0516.49003

[12] Giaquinta M., Introduction to Regularity Theory for Nonlinear Elliptic Systems, Birkhäuser, Basel, 1993. | MR 1239172 | Zbl 0786.35001

[13] Giaquinta M., Modica G., Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math. 311 (1979) 145-169. | MR 549962 | Zbl 0409.35015

[14] Giaquinta M., Modica G., Partial regularity of minimizers of quasiconvex integrals, Ann. Inst. Henri Poincaré, Analyse non Linéaire 3 (1986) 185-208. | Numdam | MR 847306 | Zbl 0594.49004

[15] Guidorzi M., Poggiolini L., Lower semicontinuity of quasiconvex integrals of higher order, Nonlinear Differ. Equations Appl. 6 (1999) 227-246. | MR 1691445 | Zbl 0930.35059

[16] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1983. | MR 737190 | Zbl 1042.35002

[17] Marcellini P., Approximation of quasiconvex functions and lower semicontinuity of multiple integrals, Manuscripta Math. 51 (1985) 1-28. | MR 788671 | Zbl 0573.49010

[18] Meyers N.G., Quasi-convexity and lower semi-continuity of multiple variational integrals of any order, Trans. Amer. Math. Soc. 119 (1965) 125-149. | MR 188838 | Zbl 0166.38501

[19] Morrey C.B., Quasiconvexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952) 25-53. | MR 54865 | Zbl 0046.10803

[20] Simon L., Lectures on Geometric Measure Theory, Australian National University Press, 1983. | MR 756417 | Zbl 0546.49019

[21] Simon L., Theorems on Regularity and Singularity of Energy Minimizing Maps, Birkhäuser, Basel, 1996. | MR 1399562 | Zbl 0864.58015

[22] Zhou X.P., Weak lower semicontinuity of a functional with any order, J. Math. Anal. Appl. 221 (1998) 217-237. | MR 1619142 | Zbl 0919.49011