Partial regularity results for minimizers of quasiconvex functionals of higher order

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 19, Issue 1, 2002, Pages 81-112

  Kronz, Manfred ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; HARMONIC ANALYSIS; MAPS;

INEQUALITIES; QUASICONVEX FUNCTIONALS;

FUNCTIONS;

EID: 0009941105     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(01)00072-5     Document Type: Article

References (22)

1. Acerbi E., Fusco N. Semicontinuity of problems in the calculus of variations. Arch. Rat. Mech. Anal. 86:1984;125-145.
2. Ball J.M. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63:1977;337-403.
3. Campanato S. Proprietà di una famiglia di spazi funzionali. Ann. Scoula Norm. Sup. Pisa. 18:1964;137-160.
4. h,α . Ann. Scoula Norm. Sup. Pisa. 18:1964;345-360.
5. 2,λ . Ann. Mat. Pura Appl. 69:1965;321-381.
6. Campanato S. Alcune osservazioni relative alle soluzioni di equazioni ellittiche di ordine 2m. Atti Convegno Equaz. Der. Parz., Bologna. 1967;17-25.
7. Dacorogna B. Direct Methods in the Calculus of Variations. 1989;Springer, Berlin.
8. Duzaar F., Steffen K., Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, preprint.
9. Evans L.C. Quasiconvexitity and partial regularity in the calculus of variations. Arch. Rat. Mech. Anal. 95:1986;227-252.
10. Evans L.C., Gariepy R.F. Measure Theory and Fine Properties of Functions. 1992;CRC Press, Boca Raton.
11. Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. 1983;Princeton University Press, Princeton.
12. Giaquinta M. Introduction to Regularity Theory for Nonlinear Elliptic Systems. 1993;Birkhäuser, Basel.
13. Giaquinta M., Modica G. Regularity results for some classes of higher order nonlinear elliptic systems. J. Reine Angew. Math. 311:1979;145-169.
14. Giaquinta M., Modica G. Partial regularity of minimizers of quasiconvex integrals. Ann. Inst. Henri Poincaré, Analyse non Linéaire. 3:1986;185-208.
15. Guidorzi M., Poggiolini L. Lower semicontinuity of quasiconvex integrals of higher order. Nonlinear Differ. Equations Appl. 6:1999;227-246.
16. Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. 1983;Springer, Berlin.
17. Marcellini P. Approximation of quasiconvex functions and lower semicontinuity of multiple integrals. Manuscripta Math. 51:1985;1-28.
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.
19. Morrey C.B. Quasiconvexity and the lower semicontinuity of multiple integrals. Pacific J. Math. 2:1952;25-53.
20. Simon L. Lectures on Geometric Measure Theory. 1983;Australian National University Press.
21. Simon L. Theorems on Regularity and Singularity of Energy Minimizing Maps. 1996;Birkhäuser, Basel.
22. Zhou X.P. Weak lower semicontinuity of a functional with any order. J. Math. Anal. Appl. 221:1998;217-237.