@article{ZNSL_2004_310_a9,
author = {M. A. Sychev},
title = {Young measures as measurable functions and applications to variational problems},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {191--212},
year = {2004},
volume = {310},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a9/}
}
M. A. Sychev. Young measures as measurable functions and applications to variational problems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 191-212. http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a9/
[1] E. Acerbi, N. Fusco, “Semicontinuity problems in the calculus of variations”, Arch. Rat. Mech. Anal., 86 (1984), 125–145 | DOI | MR | Zbl
[2] J. M. Ball, “Convexity conditions and existence theorems in nonlinear elasticity”, Arch. Rat. Mech. Anal., 63 (1978), 337–403 | DOI | MR
[3] J. M. Ball, Some open problems in Elasticity. Geometry, Mechanics, and Dynamics, Springer, New York, 2002 | MR | Zbl
[4] J. M. Ball, “A version of the fundamental theorem for Young measures”, PDE's and Continuum Models of Phase Transitions, Lecture Notes in Physics, 344, eds. M. Rascle, D. Serre, M. Slemrod, Springer-Verlag, 1989, 207–215 | MR | Zbl
[5] E. J. Balder, “A general approach to lower semicontinuity and lower closure in optimal control theory”, SIAM J. Control and Optimization, 22 (1984), 570–598 | DOI | MR | Zbl
[6] H. Berliocchi, J. M. Lasry, “Intégrandes normales et mesures paramétrées en calcul des variations”, Bull. Soc. Math. France, 101 (1973), 129–184 | MR | Zbl
[7] G. Bouchitte, I. Fonseca, J. Maly, “The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent”, Proc. Royal Soc. Edinb. Sect A, 128 (1998), 463–497 | MR
[8] J. M. Ball, R. D. James, “Fine mixtures as minimizers of energy”, Arch. Rational Mech. Anal., 100 (1987), 13–52 | DOI | MR | Zbl
[9] J. M. Ball, F. Murat, “$W^{1,p}$-quasiconvexity and variational problems for multiple integrals”, J. Funct. Anal., 58 (1984), 225–253 | DOI | MR | Zbl
[10] N. N. Bogolubov, “Sur quelques methods novelles dans le calculus des variations”, Ann. Math. Pura Appl., 7:4 (1930), 149–271
[11] P. Cardaliaquet, R. Tahraoui, “Sur léquaivalence de la 1-rang convexité et de la polyconvexité des ensembles isotropiques de $R^{2\times2}$”, C. R. Acad. Sci. Paris, Sér I, 331 (2000), 851–856 | MR
[12] L. Carbone, R. De Arcangelis, “On a non-standard convex regularization and the relaxation of unbounded integral functionals of the calculus of variations”, J. Conv. Anal., 6 (1999), 141–162 | MR | Zbl
[13] C. Castaing, M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, 580, Springer-Verlag, Berlin-New York, 1977 | MR | Zbl
[14] B. Dacorogna, Direct methods in the Calculus of Variations, Springer-Verlag, 1989 | MR
[15] I. Ekeland, R. Temam, Convex analysis and variational problems, North-Holland, 1976 | MR | Zbl
[16] T. Iwaniec, “Nonlinear analysis and quasiconformal mappings from the perspective of PDE”, Quasiconformal geometry and dynamics (Lublin, 1996), Polish Acad. Sci., 48, Banach Center Publ., Warsaw, 1999, 119–140 | MR | Zbl
[17] T. Iwaniec, C. Sbordone, “Quasiharmonic fields”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18:5 (2001), 519–572 | DOI | MR | Zbl
[18] T. Iwaniec, G. Verchota, A. Vogel, “The failure of rank-one connections”, Arch. Ration. Mech. Anal., 163:2 (2002), 125–169 | DOI | MR | Zbl
[19] R. James, S. Spector, “Remarks on $W^{1,p}$-quasiconvexity, interpenetration of matter and function spaces for elasticity”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 9 (1992), 263–280 | MR | Zbl
[20] D. Kinderlehrer, P. Pedregal, “Characterization of Young measures generated by gradients”, Arch. Rat. Mech. Anal., 115 (1991), 329–365 | DOI | MR | Zbl
[21] D. Kinderlehrer, P. Padregal, “Weak convergence of sequences and the Young measure representation”, SIAM J. Math. Anal., 23 (1992), 1–19 | DOI | MR | Zbl
[22] D. Kinderlehrer and P. Pedregal, “Gradient Young measures generated by sequences in Sobolev spaces”, J. Geom. Anal., 4:1 (1994), 59–90 | MR | Zbl
[23] K. Kuratowski, Ryll-Nardzewski, “A general theorem of selectors”, Bull. Acad. Polon. Sci., 13:6 (1966), 397–403 | MR
[24] J. Maly, “Weak lower semicontinuity of polyconvex integrals”, Proc. Royal Soc. Edinburgh A, 123 (1993), 681–691 | MR | Zbl
[25] C. Morrey, Multiple integrals in the Calculus of Variations, Springer-Verlag, 1966 | MR | Zbl
[26] P. Pedregal, Parametrized measures and variational principles, Progress in Nonlinear Differential Equations and their Applications, 30, Birkhäuser, Basel, 1997 | MR | Zbl
[27] Yu. G. Reshetnyak, “Obschie teoremy o polunepreryvnosti i skhodimosti s funktsionalom”, SMZh, 8 (1967), 1052–1071 | MR
[28] M. A. Sychev, “Neobkhodimye i dostatochnye usloviya v teoremakh o polunepreryvnosti snizu i skhodimosti s funktsionalom”, Mat. Sb., 186:6 (1995), 77–108 | MR | Zbl
[29] M. Sychev, A new approach to Young measure theory, relaxation and convergence in energy, Preprint 43/97/M, SISSA (Triest, Italy), March 1997 | MR
[30] M. Sychev, “Characterization of homogeneous gradient Young measures in the case of arbitrary integrands”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29 (2000), 531–548, Fasc. 3 | MR | Zbl
[31] M. Sychev, “Attainment and relaxation results in special classes of deformations”, Calc. Var., 19 (2004), 183–210 | DOI | MR | Zbl
[32] M. Sychev, Young measures as measurable functions, 2003
[33] Šilhavý, “Rotationally invariant rank-1 convex functions”, Appl. Math. Optim., 44 (2001), 1–15 | DOI | MR
[34] Šilhavý, “Monotonicity of rotationally invariant convex and rank 1 convex functions”, Proc. Royal Soc. Edinburgh A, 132 (2002), 419–435 | DOI | MR
[35] Silhavý, “An $O(n)$ invariant rank 1 convex function that is not polyconvex”, Theor. Appl. Mech., 28–29, 2002, 325–336 | MR | Zbl
[36] L. Tartar, “Compensated compactness and applications to partial differential equations”, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Pitman Research Notes in Mathematics, 4, 1979, 136–212 | MR | Zbl
[37] L. C. Young, “Generalized curves and the existence of an attained absolute minimum in the Calculus of Variations”, C. R. Soc. Sci. Varsovie, 30 (1937), 212–234 | Zbl
[38] L. C. Young, Lectures on the Calculus of Variations and Optimal Control Theory, W. B. Saunders Company, Philadelphia–London–Toronto, 1969, reprinted by Chelsea 1980 | MR | Zbl