On Hessian matrices in the space BH

Communications in Contemporary Mathematics

Volumn 7, Issue 4, 2005, Pages 401-420

  Fonseca, Irene ^a   Leoni, Giovanni ^a   Paroni, Roberto ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF SASSARI   (Italy)

Author keywords

Functions of bounded Hessian; Functions of bounded variation; N simplex; Special functions of bounded Hessian; Special functions of bounded variation; Triangulations

Indexed keywords

EID: 24144435334     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199705001805     Document Type: Article

References (31)

1. G. Alberti, A Lusin type theorem for gradients, J. Funct. Anal. 100 (1991) 110-118.
2. G. Alberti, Integral representation of local functionals, Ann. Mat. Pura Appl. 165 (1993) 49-86.
3. G. Alberti and G. Buttazzo, Local mappings on spaces of differentiable functions, Manuscripta Math. 79(1) (1993) 81-97.
4. G. Alberti and G. Mantegazza, A note on the theory of SB V functions, Boll. Unione Mat Ital. B11 (1997) 375-382.
5. L. Ambrosio, A compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. Ital. 3B7 (1989) 857-881.
6. L. Ambrosio, Existence theory for a new class, Arch. Rat. Mech. Anal. 111 (1990) 291-322.
7. k), Nonlinear Anal. 23 (1994) 405-425.
8. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Mathematical Monographs (Oxford University Press, 2000).
9. J. M. Ball and R. D. James, Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987) 13-52.
10. A. Braides, Approximation of Free-Discontinuity Problems, Lectures Notes in Mathematics, Vol. 1694 (Springer-Verlag, 1999).
11. m), J. Math. Pures Appl. 75 (1996) 595-626.
12. A. Braides and A. Defranceschi, Homogenization of Multiple Integrals (Clarendon Press, Oxford, 1998).
13. M. Carriero, A. Leaci and F. Tomarelli, Special bounded Hessian and elastic-plastic plate, Rend. Accad. Naz. Sci. XL Mem. Mat. 16(5) (1992) 223-258.
14. M. Carriero, A. Leaci and F. Tomarelli, A second order model in image segmentation, in Blake & Zisserman functional, Progress in Nonlinear Differential Equations and Their Applications, Vol. 25 (Birkhäuser, 1996), pp. 57-72.
15. R. Choksi and I. Fonseca, Bulk and interfacial energy densities for structured deformations of continua, Arch. Rational Mech. Anal. 138 (1997) 37-103.
16. R. Choksi, R. V. Kohn and F. Otto, Domain branching in uniaxial ferromagnets: a scaling law for the minimum energy, Commun. Math. Phys. 201 (1999) 61-79.
17. P. G. Ciarlet, Numerical Analysis of the Finite Element Method (Les Presses de l'Université de Montréal, 1976).
18. S. Conti, I. Fonseca and G. Leoni, A Γ-convergence result for the two-gradient theory of phase transitions, Commun. Pure Appl. Math. 55 (2002) 857-936.
19. E. De Giorgi and L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. 82(8) (1988) 199-210.
20. G. Del Piero and D. R. Owen, Structured deformations of continua, Arch. Rational Mech. Anal. 124 (1993) 99-155.
21. G. Del Piero and L. Truskinovsky, Macro- and micro-cracking in one-dimensional elasticity, Int. J. Solids Struct. 38 (2001) 1135-1148.
22. F. Demengel, Fonctions á hessien borné, Ann. Inst. Fourier (Grenoble) 34 (1984) 155-190.
23. F. Demengel, Compactness theorems for spaces of functions with bounded derivatives and applications to limit analysis problems in plasticity, Arch. Rational Mech. Anal. 105 (1989) 123-161.
24. A. De Simone, Energy minimizers for large ferromagnetic bodies, Arch. Rat. Mech. Anal. 125 (1993) 99-143.
25. I. Fonseca, and G. Leoni, Modern Methods in the Calculus of Variations with Applications to Nonlinear Continuum Physics, to appear in the Applied Mathematical Sciences Series (Springer-Verlag, 2006).
26. W. Jin and R. V. Kohn, Singular perturbation and the energy of folds, J. Nonlinear Sci. 10 (2000) 355-390.
27. R. V. Kohn and S. Müller, Surface energy and microstructure in coherent phase transitions, Commun. Pure. Appl. Math. 47 (1994) 405-435.
28. A. P. Morse, Perfect blankets, Trans. Amer. Math. Soc. 61 (1947) 418-442.
29. S. Müller, Variational Models for Microstructures and Phase Transitions, Lecture Notes (MPI Leipzig, 1998).
30. D. R. Owen and R. Paroni, Second-order structured deformations, Arch. Rational Mech. Anal. 155 (2000) 215-235.
31. R. Temam, Problémes Mathématiques en Plasticité (Gauthier-Villars, Paris, 1983).