Characterization of homogeneous gradient young measures in case of arbitrary integrands
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)
- Volume: 29, Issue: 3, page 531-548
- ISSN: 0391-173X
Access Full Article
topHow to cite
topSychev, Mikhail A.. "Characterization of homogeneous gradient young measures in case of arbitrary integrands." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.3 (2000): 531-548. <http://eudml.org/doc/84417>.
@article{Sychev2000,
author = {Sychev, Mikhail A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Young measures; calculus of variations; integral functionals; relaxation},
language = {eng},
number = {3},
pages = {531-548},
publisher = {Scuola normale superiore},
title = {Characterization of homogeneous gradient young measures in case of arbitrary integrands},
url = {http://eudml.org/doc/84417},
volume = {29},
year = {2000},
}
TY - JOUR
AU - Sychev, Mikhail A.
TI - Characterization of homogeneous gradient young measures in case of arbitrary integrands
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 3
SP - 531
EP - 548
LA - eng
KW - Young measures; calculus of variations; integral functionals; relaxation
UR - http://eudml.org/doc/84417
ER -
References
top- [AF] E. Acerbi - N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal. 86 (1984), 125-145. Zbl0565.49010MR751305
- [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. Zbl0549.49005MR747970
- [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. Zbl0991.49500MR1036070
- [B2] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1978), 337-403. Zbl0368.73040MR475169
- [B3] J.M. Ball, Review of "Nonlinear problems of elasticity" by Stuart Antman.Bull., AMS3 (1996), 269-276.
- [BL] H. Berliocchi - J.M. Lasry, Intégrandes normales et mesures paramétrées en calcul des variations, Bull. Soc. Math. France101 (1973), 129-184. Zbl0282.49041MR344980
- [BM] J.M. Ball - F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal.58 (1984), 225-253. Zbl0549.46019MR759098
- [Bu] G. Buttazzo, "Lower Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations", Pitman Res. Notes Math. Ser. 207, 1989. Zbl0669.49005MR1020296
- [C] P. Ciarlet, "Mathematical Elasticity", Vol.I: "Three-Dimensional Elasticity", North-Holland, 1988. Zbl0648.73014MR936420
- [D] B. Dacorogna, "Direct Methods in the Calculus of Variations ", Springer-Verlag, 1989. Zbl0703.49001MR990890
- [ET] I. Ekeland - R. Temam R., "Convex analysis and variational problems ", North-Holland, 1976. Zbl0322.90046MR463994
- [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 Linéaire14 (1997), 309-338. Zbl0868.49011MR1450951
- [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 Linéaire9 (1992), 263-280. Zbl0773.73022MR1168303
- [KP1] D. Kinderlehrer - P. Pedregal, Characterization of Young measures generated by gradients, Arch. Rational Mech. Anal.115 (1991), 329-365. Zbl0754.49020MR1120852
- [KP2] D. Kinderlehrer - P. Pedregal, Weak convergence of integrands and the Young measure representation, SIAM J. Math. Anal.23 (1992), 1-19. Zbl0757.49014MR1145159
- [KP3] D. Kinderlehrer - P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal.4 (1994), 59-90. Zbl0808.46046MR1274138
- [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. A123 (1993), 681-691. Zbl0813.49017MR1237608
- [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 Linéaire11 (1994), 217-243. Zbl0863.49002MR1267368
- [Sa] S. Saks, "Theory of the integral", Hafner, New York, 1937. Zbl0017.30004
- [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 Linéaire15 (1998), 755-782. Zbl0923.49009MR1650962
- [S2] M. Sychev, A new approach to Young measure theory, relaxation and convergence in energy, Ann. Inst. H. Poincaré Anal. Non Linéaire16 (1999), 773-812. Zbl0943.49012MR1720517
- [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. MR1870168
- [Sv1] V Šverák, New examples of quasiconvex functions, Arch. Rational Mech. Anal.119 (1992), 293-300. Zbl0823.26009MR1179688
- [Sv2] V Šverák, On Tartar's conjecture, Ann. Inst. H. Poincaré Anal. Non Linéaire10 (1993), 405-412. Zbl0820.35022MR1246459
- [Sv3] V Šverák, Regularity properties of deformations with finite energy, Arch. Rational Mech. Anal.100 (1988), 105-127. Zbl0659.73038MR913960
- [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. Zbl0437.35004MR584398
- [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. Zbl0536.35003MR725524
- [Y] L.C. Young, "Lectures on the Calculus of Variations and Optimal Control Theory", Saunders, 1969 (reprinted by Chelsea1980). Zbl0177.37801MR259704
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.