On young measures controlling discontinuous functions

Journal of Convex Analysis

Volumn 13, Issue 1, 2006, Pages 177-192

  Kalamajska, Agnieszka ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Discontinuous functions; Weak convergence; Young measures

Indexed keywords

EID: 33645153846     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. J. J. Alibert, G. Bouchitte: Non-uniform integrability and generalized Young measures, J. Convex Analysis 4(1) (1997) 129-147.
2. J. P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhäuser, Boston (1990).
3. E. Balder: Lectures on Young measure theory and its applications to economics, Rend. Inst. Mat. Univ. Trieste 31(1) (2000) 1-69.
4. J. M. Ball: A version of the fundamental theorem for Young measures, in: PDE's and Continuum Models of Phase Transitions, M. Rascle, D. Serre, M. Slemrod (eds.), Lecture Notes in Physics 334, Springer, Berlin (1989) 207-215.
5. P. G. Ciarlet: Mathematical Elasticity, Vol I: Three-Dimensional Elasticity, North-Holland, Amsterdam (1988).
6. A. G. Chentsov, S. I. Morina: Extensions and Relaxations, Kluwer, Dordrecht (2002).
7. R. J. DiPerna: Measure-valued solutions to conservation laws in continuum physics, Arch. Rational Mech. Anal. 88(3) (1985) 223-227.
8. R. J. DiPerna, A. J. Majda: Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987) 667-689.
9. L. C. Evans: Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS 74, AMS, Providence (1990).
10. H. O. Fattorini: Infinite-Dimensional Optimization and Control Theory, Encyclopedia of Mathematics and its Applications 62, Cambridge University Press, Cambridge (1999).
11. T. Gimse: Conservation laws with discontinuous flux functions, SIAM J. Math. Anal. 24(2) (1993) 279-289.
12. P. Gwiazda: An existence result for a model of granular material with non-constant density, Asympt. Anal. 30 (2002) 43-60.
13. P. Gwiazda, A. Zatorska-Goldstein: An existence results for the Leray-Lions type operators with discontinuous coefficients, Asympt. Anal., to appear.
14. R. E. Gladfelter, S. P. Gupta: Effect for fractional flow hysteresis on recovery of tertiary oil, SPD J. (Dec. 1980) 508-520.
15. J. M. N. T. Gray, M. Wieland, K. Hutter: Gravity-driven free surface flow of granular avalanches over complex basal topography, Proc. R. Soc. Lond., Ser. A 445 (1999) 1841-1874.
16. N. Hungerbühler. A refinement of Ball's theorem on Young measures, New York J. Math. 3 (1997) 48-53.
17. K. Hutter, S. Savage: The motion of a finite mass of granular material down a rough incline, J. Fluid Mech. 199 (1989) 177-215.
18. A. Katamajska: Between the classical theorem of Young and convergence theorem in setvalued analysis, in preparation.
19. T. Koch, R. Greve, K. Hutter: Unconfined flow of granular avalanches along a partly curved surface. II: Experiments and numerical computations, Proc. R. Soc. Lond., Ser. A 445 (1994) 399-413.
20. p-Young measures, J. Math. Anal. Appl. 198 (1996) 830-843.
21. M. Kružík, T. Roubíček: On the measures of Diperna and Majda, Math. Bohemica 122 (1997) 383-399.
22. K. Kuratowski: Topologia, Monografie Matematyczne Tom 21, Państwowe Wydawnictwo Naukowe, Warsaw (1961), (in Polish).
23. M. J. Lighthill, G. B. Whitham: On kinematic waves. I. Flood movement in long rivers, Proc. R. Soc. Lond., Ser. A 229 (1955) 281-316; II.
24. Theory of traffic flow on long crowded roads, Proc. R. Soc. Lond., Ser. A 229 (1955) 317-345.
25. B. B. Maini, T. Okazawa: Effects of temperature on heavy oil-vater relative permeability of sand, J. Can. Pet. Tech. 26 (1987) 33-41.
26. J. Málek, J. Necas, M. Rokyta, M. Ruzicka: Weak and Measure-Valued Solutions to Evolutionary PDE's, Chapman & Hall, London (1996).
27. D. Marchesin, H. B. Medeiros, P. J. Paes-Leme: A model for two phase flow with hysteresis, Contemp. Math. 60 (1987) 89-107.
28. S. Migórski, A. Ochal: Optimal control of parabolic hemivariational inequalities, J. Global Optim. 17 (2000) 285-300.
29. S. Müller: Variational models for microstructure and phase transitions, in: Calculus of Variations and Geometric Evolution Problems, S. Hildebrandt, M. Struwe (eds.), Lectures Notes in Mathematics 1713, Springer, Berlin (1999).
30. H. Nagahama, R. Teisseyre: Dislocation field evolution and dislocation source / sink function, Acta Geophys. Pol. 46(1) (1998) 13-33.
31. Z. Naniewicz, P. D. Panagiotopoulos: Mathematical Theory of Hemivariational Inequalities and Applications, Marcel Dekker, New York (1995).
32. P. Pedregal: Parametrized Measures and Variational Principles, Birkhäuser, Basel (1997).
33. K. Pruess, Y. W. Tsang: On two-phase relative permeability and capillary pressure of rough-walled rock fractures, Water Resour. Res. 26 (1990) 1915-1926.
34. Yu. G. Reshetnyak: Weak convergence of completely additive vector functions on a set, Siberian Math. J. 9 (1968) 1039-1045,
35. Translation of Sibirsk. Mat. Z. 9 (1968) 1386-1394.
36. T. Roubíček: Relaxation in Optimalization Theory and Variational Calculus, W. de Gruyter, Berlin (1997).
37. W. Rudin: Real and Complex Analysis, McGraw-Hill, New York (1966).
38. W. R. Schowalter: Mechanics of Non-Newtonian Fluids, Pergamon Press, Oxford (1978).
39. K. Yosida: Functional Analysis, Springer, Berlin (1965).
40. L. C. Young: Generalized curves and the existence of an attainment absolute minimum in the calculus of variations, C. R. Soc. Sci. Lett. Varsovie, III 30 (1937) 212-234.