Characterization of homogeneous gradient young measures in case of arbitrary integrands
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, p. 531-548 
@article{ASNSP_2000_4_29_3_531_0,
     author = {Sychev, Mikhail A.},
     title = {Characterization of homogeneous gradient young measures in case of arbitrary integrands},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {3},
     year = {2000},
     pages = {531-548},
     zbl = {1067.49009},
     mrnumber = {1817708},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_3_531_0}
}

Sychev, Mikhail A. Characterization of homogeneous gradient young measures in case of arbitrary integrands. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, pp. 531-548. http://www.numdam.org/item/ASNSP_2000_4_29_3_531_0/

[AF] E. Acerbi - N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. | MR 751305 | Zbl 0565.49010

[Ba] E.J. Balder, A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control Optim. 22 (1984), 570-598. | MR 747970 | Zbl 0549.49005

[B1] 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, Vol. 344, Springer-Verlag, 1989, pp. 207-215. | MR 1036070 | Zbl 0991.49500

[B2] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1978), 337-403. | MR 475169 | Zbl 0368.73040

[B3] J.M. Ball, Review of "Nonlinear problems of elasticity" by Stuart Antman. Bull., AMS 3 (1996), 269-276.

[BL] H. Berliocchi - J.M. Lasry, Intégrandes normales et mesures paramétrées en calcul des variations, Bull. Soc. Math. France 101 (1973), 129-184. | Numdam | MR 344980 | Zbl 0282.49041

[BM] J.M. Ball - F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225-253. | MR 759098 | Zbl 0549.46019

[Bu] G. Buttazzo, "Lower Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations", Pitman Res. Notes Math. Ser. 207, 1989. | MR 1020296 | Zbl 0669.49005

[C] P. Ciarlet, "Mathematical Elasticity", Vol.I: "Three-Dimensional Elasticity", North-Holland, 1988. | MR 936420 | Zbl 0648.73014

[D] B. Dacorogna, "Direct Methods in the Calculus of Variations ", Springer-Verlag, 1989. | MR 990890 | Zbl 0703.49001

[ET] I. Ekeland - R. Temam R., "Convex analysis and variational problems ", North-Holland, 1976. | MR 463994 | Zbl 0322.90046

[FM] I. Fonseca - J. Maly, Relaxation of Multiple Integrals in Sobolev Spaces Below the Growth Exponent for the Energy Density, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), 309-338. | Numdam | MR 1450951 | Zbl 0868.49011

[JS] R.D. James - S.J. Spector, Remarks on W1,p-quasiconvexity, interpenetration of matter and function spaces for elasticity, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), 263-280. | Numdam | MR 1168303 | Zbl 0773.73022

[KP1] D. Kinderlehrer - P. Pedregal, Characterization of Young measures generated by gradients, Arch. Rational Mech. Anal. 115 (1991), 329-365. | MR 1120852 | Zbl 0754.49020

[KP2] D. Kinderlehrer - P. Pedregal, Weak convergence of integrands and the Young measure representation, SIAM J. Math. Anal. 23 (1992), 1-19. | MR 1145159 | Zbl 0757.49014

[KP3] D. Kinderlehrer - P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal. 4 (1994), 59-90. | MR 1274138 | Zbl 0808.46046

[Kr] J. Kristensen, Finite functionals and Young measures generated by gradients of Sobolev functions, Ph.D. Thesis, Technical University of Denmark, Kyngby, August 1994.

[M] J. Maly, Weak lower semicontinuity of polyconvex integrals, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 681-691. | MR 1237608 | Zbl 0813.49017

[MQY] S. Müller - T. Qi - B.S. Yan, On a new class of elastic deformations not allowing for cavitation, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994), 217-243. | Numdam | MR 1267368 | Zbl 0863.49002

[Sa] S. Saks, "Theory of the integral", Hafner, New York, 1937. | Zbl 0017.30004

[S1] M. Sychev, Young measure approach to characterization of behavior of integral functionals on weakly convergent sequences by means of their integrands, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 755-782. | Numdam | MR 1650962 | Zbl 0923.49009

[S2] M. Sychev, A new approach to Young measure theory, relaxation and convergence in energy, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 773-812. | Numdam | MR 1720517 | Zbl 0943.49012

[S3] M. Sychev, Young measures as measurable functions, (in preparation).

[S4] M. Sychev, Existence and relaxation results in special classes of deformations, Preprint No 17, Max-Planck-Institute for Mathematics in Sciences, Leipzig, February 2000. | MR 1870168

[Sv1] V Šverák, New examples of quasiconvex functions, Arch. Rational Mech. Anal. 119 (1992), 293-300. | MR 1179688 | Zbl 0823.26009

[Sv2] V Šverák, On Tartar's conjecture, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 405-412. | Numdam | MR 1246459 | Zbl 0820.35022

[Sv3] V Šverák, Regularity properties of deformations with finite energy, Arch. Rational Mech. Anal. 100 (1988), 105-127. | MR 913960 | Zbl 0659.73038

[T1] L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Pitman Res. Notes Math. Ser. 39, 1979, pp. 136-212. | MR 584398 | Zbl 0437.35004

[T2] L. Tartar, The compensated compactness method applied to systems of conservations laws, in Systems of Nonlinear Partial Differential Equations, J. M. Ball (ed.), NATO ASI Series, Vol. CIII, Reidel, 1982. | MR 725524 | Zbl 0536.35003

[Y] L.C. Young, "Lectures on the Calculus of Variations and Optimal Control Theory", Saunders, 1969 (reprinted by Chelsea 1980). | MR 259704 | Zbl 0177.37801