Superposition and Chain Rule for Bounded Hessian Functions

Advances in Mathematics

Volumn 140, Issue 2, 1998, Pages 237-281

  Savaré, Giuseppe ^a   Tomarelli, Franco ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040005840     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1770     Document Type: Article

References (27)

1. Alberti G. Rank one property for derivatives of functions with bounded variation. Proc. Roy. Soc. Edinburgh, Sect. A. 123:1993;239-274.
2. Ambrosio L. A compactness theorem for a special class of functions of bounded variation. Boll. Un. mat. Ital. 3-B:1989;857-881.
3. Ambrosio L. Variational problems in SBV. Acta Appl. Math. 17:1989;1-40.
4. Ambrosio L., Dal Maso G. A general chain rule for distributional derivatives. Proc. A.M.S. 108:1990;691-702.
5. Bourdaud G. Sur les opérateurs pseudo-differentiels à coefficients peu réguliers. 1983;Univ. de Paris Sud.
6. Bourdaud G., Meyer Y. Fonctions que opèrent sur les espaces de Sobolov. J. Functional Anal. 97:1991;351-360.
7. Brezis H. Opérateurs maximaux et sémi-groupes de contractions dans les espaces de Hilbert. 1973;North Holland, Amsterdam.
8. Carriero M., Leaci A., Tomarelli F. Special bounded hessian and elastic-plastic plate. Rend. Accad. Naz. Sci. dei XL, Mem. Mat. XVI:1992;223-258.
9. Carriero M., Leaci A., Tomarelli F. A second order model in image segmentation: Blak & Zisserman functional. Variational Methods for Discontinuous Structures. 1996;Birkhäuser, Basel. p. 57-72.
10. Dal Maso G., Le Floch P., Murat F. Definition and weak stability of nonconservative products. Publ. Lab. d 'Analyse Numerique, Univ. P. & M. Curie. 13:1994;1-65.
11. De Giorgi E. Movimenti di partizioni. Serapioni R., Tomarelli F. Variational Methods for Discontinuous Structures. 1996;1-4 Birkhäuser, Basel.
12. Delfour M. C., Zolésio J. P. Shape analysis via oriented distance functions. J. Funct. Anal. 86:1989;129-201.
13. Demengel F. Fonctions a Hessian Borné Ann. Inst. Fourier. 34:1984;155-190.
14. Ekeland I., Temam R. Analyse Convexe et problèmes variationnels. 1974;Dunod, Paris.
15. Evans L. C., Gariepy R. F. Measure Theory and Fine Properties of Functions. Studies in Adv. Math. 1992;CRC Press, Boca Raton.
16. Federer H. Geometric Measure Theory. 1969;Springer-Verlag, Berlin.
17. Giusti E. Minimal Surfaces and Functions of Bounded Variation. 1984;Birkhäuser, Boston.
18. Marcus M., Mizel V. J. Absolute continuity on tracks and mappings of Sobolev spaces. Arch. Rational Mech. Anal. 45:1972;294-320.
19. Rudin W. Real and Complex Analysis. 1974;McGraw-Hill, New York.
20. Runst T., Sickel W. Sobolev Spaces of Fractional Order, Nemytzkij Operators and Nonlinear Partial Differential Equations. 1996;de Gruyter, Berlin.
21. Savaré G. On the regularity of the positive part of functions. Nonlin. Anal. 27:1996;1055-1074.
22. Stampacchia G. Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble). 15:1965;189-258.
23. Stein E. M. Singular Integrals and Differentiability Properties of Functions. 1970;Princeton Univ. Press, Princeton.
24. Temam R. Problèmes mathématiques en plasticité 1983;Dunod, Paris.
25. Tomarelli F. A quasi-variational problem in nonlinear elasticity. Ann. Mat. Pura Appl. (IV). 158:1991;331-389.
26. Vol'pert A. I. The spacesBV. Math. USSR-Sb. 2:1967;225-267.
27. Ziemer W. P. Weakly Differentiable Functions. 1988;Springer-Verlag, New York.