On the regularity of the positive part of functions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 27, Issue 9, 1996, Pages 1055-1074

  Savaré, Giuseppe ^a  

^a CNR   (Italy)

Author keywords

Functions with gradient of bounded variation; Intermediate Sobolev and Besov spaces; Truncations

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; DIFFERENTIATION (CALCULUS); FUNCTIONS; INTERPOLATION; VARIATIONAL TECHNIQUES; VECTORS;

BANACH SPACES; BESOV SPACES; HESSIAN DEPENDENT FUNCTIONAL; HILBERTIAN FRAMEWORK; K METHOD OF PEETRE; LIPSCHITZ OPEN SET; MATRIX VALUED BOUNDED MEASURE; POINCARE TYPE INEQUALITY; REGULARITY PROPERTIES; TRUNCATION OPERATOR;

MATHEMATICAL OPERATORS;

EID: 0030295631     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(95)00104-4     Document Type: Article

References (24)

1. STAMPACCHIA G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier Univ. Grenoble 15, 189-258 (1965).
2. MARCUS M. & MIZEL V. J., Absolute continuity on tracks and mappings of Sobolev spaces, Archs ration. Mech. Analysis 45, 294-320 (1972).
3. AMBROSIO L. & DAL MASO G., A general chain rule for distributional derivatives, Proc. Am. math. Soc. 108, 691-702 (1990).
4. ADAMS R., Sobolev Spaces. Academic Press, New York (1975).
5. NIKOLŚKII S. M., Approximation of Functions of Several Variables and Imbedding Theorems. Springer, Berlin (1975).
6. TRIEBEL H., Theory of Function Spaces, II. Birkhäuser, Boston (1992).
7. BERGH P. L. & LÖFSTRÖM J., Interpolation Spaces. Springer, Berlin (1976).
8. BUTZER P. L. & BERENS H., Semi-groups of Operators and Approximation. Springer, Berlin (1967).
9. BOURDAUD G. & MEYER Y., Fonctions qui opèrent sur les espaces de Sobolev, J. funct. Analysis 97, 351-360 (1991).
10. LIONS J.-L. & MAGENES E., Non Homogeneous Boundary Value Problems and Applications I. Springer, Berlin (1972).
11. DEMENGEL F., Fonctions a Hessian Borné, Ann. Inst. Fourier Univ. Grenoble 34, 155-190 (1984).
12. CARRIERO M., LEACI A. & TOMARELLI F., Special bounded hessian and elastic-plastic plate, R. Accad. Naz. Sci. dei XL, Mem. Mat. XVI, 223-258 (1992).
13. GAGLIARDO E., A unified structure in various families of function spaces. Compactness and closure theorems, Proc. Int. Symp. Linear Spaces, Jerusalem, pp. 237-241. Jerusalem Academic Press (1960).
14. FEDERER H., Geometric Measure Theory. Springer, Berlin (1969).
15. GIUSTI E., Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston (1984).
16. TARTAR L., Remarks on some interpolation spaces, in Boundary Value Problems for PDEs and Applications (Edited by C. BAIOCCHI and J.-L. LIONS), pp. 229-252. Masson, Paris (1993).
17. TARTAR L., Interpolation non linéaire et régularité, J. funct. Analysis 9, 468-489 (1972).
18. SAVARÉ G., Weak solutions and maximal regularity for abstract inequalities, Adv. Math. Sci. Appl. (to appear).
19. VISINTIN A., Stefan problem with phase relaxation, I.M.A. J. Appl. Math. 34, 225-245 (1985).
20. SAVARÉ G., Approximation and regularity of evolution variational inequalities, Rc. Acc. Naz. Sci. dei XL, Mem. Mat. XVII, 83-111 (1993).
21. ZIEMER W. P., Weakly Differentiable Functions. Springer, New York (1988).
22. LIONS J.-L. & PEETRE J., Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19, 5-68 (1964).
23. TEMAM R., Problèmes mathématiques en plasticité. Dunod, Paris (1983).
24. STEIN E. M., Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, N.J. (1970).