Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
@article{BUMI_2007_8_10B_1_a8, author = {Gargiulo, Giuliano and Zappale, Elvira}, title = {The {Energy} {Density} of {Non} {Simple} {Materials} {Grade} {Two} {Thin} {Films} via a {Young} {Measure} {Approach}}, journal = {Bollettino della Unione matematica italiana}, pages = {159--194}, publisher = {mathdoc}, volume = {Ser. 8, 10B}, number = {1}, year = {2007}, zbl = {1129.74028}, mrnumber = {2310963}, language = {en}, url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a8/} }
TY - JOUR AU - Gargiulo, Giuliano AU - Zappale, Elvira TI - The Energy Density of Non Simple Materials Grade Two Thin Films via a Young Measure Approach JO - Bollettino della Unione matematica italiana PY - 2007 SP - 159 EP - 194 VL - 10B IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a8/ LA - en ID - BUMI_2007_8_10B_1_a8 ER -
%0 Journal Article %A Gargiulo, Giuliano %A Zappale, Elvira %T The Energy Density of Non Simple Materials Grade Two Thin Films via a Young Measure Approach %J Bollettino della Unione matematica italiana %D 2007 %P 159-194 %V 10B %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a8/ %G en %F BUMI_2007_8_10B_1_a8
Gargiulo, Giuliano; Zappale, Elvira. The Energy Density of Non Simple Materials Grade Two Thin Films via a Young Measure Approach. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 159-194. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a8/
[1] A Variational Definition of the Strain Energy for an Elastic String, J. Elasticity, 25, n. 2 (1991), 137-148. | DOI | MR | Zbl
- , ,[2] Nonlinear Problems in Elasticity, Applied Mathemathical Science, 107, Springer Verlag, New York, (1995). | DOI | MR | Zbl
,[3] Dimension reduction in variational problems, asymptotic development in $\Gamma$-convergence and thin strucutures in elasticity, Asymptot. Anal., 9, No. 1 (1994), 61-100. | MR | Zbl
- - ,[4] A version of the fundamental theorem for Young measures, PDE's and Continuum Models of Phase Transition, M. RASCLE, D. SERRE - M. SLEMROD, eds., Lecture Notes in Phys., 334, Springer-Verlag, Berlin, (1989), 207-215. | DOI | MR | Zbl
,[5] A Total-Variation Surface Energy Model for Thin Films of Martensitic Cristals, Interfaces Free Bound., 4, n. 1 (2002), 71-88. | DOI | MR | Zbl
- ,[6] A Theory of Thin Films of Martensitic Materials with Applications to Microactuators, J. Mech. Phys. Solids, 47, n. 3 (1999). | DOI | MR | Zbl
- ,[7] 3D-2D Asymptotic Analysis for Inhomogeneous Thin Films, Indiana Univ. Math. J., 49, n. 4 (2000), 1367-1404. | DOI | MR | Zbl
- - ,[8] $mathcal{A}$-quasiconvexity: relaxation and homogenization, ESAIM, Control Optim. Calc. Var., 5 (2000), 539-577. | fulltext EuDML | DOI | MR | Zbl
- - ,[9] Equi-integrability Results for 3D-2D Dimension Reduction Problems, ESAIM: Control Optim. Calc. Var., 7 (2002), 443-470. | fulltext EuDML | DOI | MR | Zbl
- ,[10] A Young Measure Approach to a Nonlinear Membrane Model Involving the Bending Moment, Proc. Royal Soc. Edimb. (2004) to appear. | DOI | MR | Zbl
- ,[11] Semicontinuity, relaxation and integral representation in the calculus of variations, Pitman Research Notes in Mathematics, 207. Harlow: Longman Scientific and Technical; New York: John Wiley and Sons. (1989). | MR
,[12] Unbounded functionals in the calculus of variations. Representations, relaxation, and homogenization, Chapman and Hall/CRC Research Notes in Mathematics, 125 Boca Raton, Chapman and Hall/CRC. xiii, (2002). | MR
- ,[13] Mathematical elasticity. Vol. II. Theory of plates. Studies in Mathematics and its Applications, 27. North-Holland Publishing Co., Amsterdam, (1997). | MR | Zbl
,[14] A Justification of the Two-Dimensional Linear Plate Model, J. Mécanique 18, n. 2 (1979), 315-344. | MR | Zbl
- ,[15] Nonclassical Elastic Solids Pitman Research Notes in Mathematics, Longman Scientific and Technical, Harlow; copublished in the United States with John Wiley and Sons, Inc., 293, New York, (1993). | MR
- ,[16] An Introduction to $\Gamma$-convergence, Birkhauser, Boston (1993). | DOI | MR | Zbl
,[17] Homogenization Limits of the Equations of Elasticity in Thin Domains, SIAM J. Math. Anal., 18 n. 2 (1987) 435-451. | DOI | MR | Zbl
- ,[18] Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 58 (8) n. 6 (1975), 842-850. | MR
- ,[19] A-quasiconvexity, Lower Semicontinuity and Young measures, SIAM J. Math. Anal., 30 (6) (1999), 1355-1390. | DOI | MR
- ,[20] The energy density of martensitic thin films via dimension reduction, Interfaces Free Bound-. 6, n. 4 (2004), 439-459. | DOI | MR | Zbl
- ,[21] A 3D-1D Young measure theory of an elastic string, Asymptotic Analysis, 39 n. 1 (2004), 61-89. | MR | Zbl
- ,[22] Rigorous Derivation of nonlinear plate theory and geometric rigidity, C. R., Math., Acad. Sci. Paris, 334, No. 2 (2002), 173-178. | DOI | MR | Zbl
- - ,[23] A Theorem on Geometric Rigidity and the derivation of nonlinear plate theory from three dimensional elasticity, Commun. Pure Appl. Math., 55, No. 11 (2002), 1461-1506. | DOI | MR | Zbl
- - ,[24] A Justification of Nonlinear Properly Invariant Plate Theories, Arch. Rational Mech. Anal., 124, n. 2 (1993), 157-199. | DOI | MR | Zbl
- - ,[25] A Remark on the Junction in a Thin Multi-Domain: the Non Convex Case, to appear on NoDEA. | DOI | MR | Zbl
, ,[26] Asymptotic analysis of a class of minimization problems in a thin multidomain, Calc. Var. Partial Differ. Equ., 15, No. 2 (2002), 181-202. | DOI | MR | Zbl
- - - ,[27] On the junction of elastic plates and beams, C. R., Math., Acad. Sci. Paris, 335, No. 8 (2002), 717-722. | DOI | MR | Zbl
- - - - ,[28] Junction in a Thin Multidomain for a Fourth Order Problem, to appear on Math. Mod. Meth. Appl. Sc. | DOI | MR | Zbl
- ,[29] Regularity Results for Some Classes of Higher Order Non-Linear Elliptic Systems, J. für reine and angew. Math., 311/312 (1979), 145-169. | fulltext EuDML | MR | Zbl
- ,[30] Theory of Diffusionless Phase Transition, Lecture Notes in Physics, 334, Springer (1989), 51-84. | DOI | MR | Zbl
- ,[31] Characterizations of Young measures generated by gradients, Arch. Rational Mech. Anal., 115 (1991), 329-265. | DOI | MR | Zbl
- ,[32] Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal., 4 (1994), 59-90. | DOI | MR | Zbl
- ,[33] The Nonlinear Membrane Model as Variational Limit of Nonlinear Three-Dimensional Elasticity, J. Math. Pures Appl., 74, n. 6 (1995), 549-578. | MR | Zbl
- ,[34] Variational Convergence for Nonlinear Shell Models with Directors and Related Semicontinuity and Relaxation Results, Arch. Rational Mech. Anal., 154, n. 2 (2000), 101-134. | DOI | MR | Zbl
- ,[35] Modeling Heterogeneous Wires Made of Martensitic Materials, C. R. Acad. Sci. Paris Sér. I. Math., 337, (2003), 143-147. | DOI | MR | Zbl
- ,[36] Modeling Heterogeneous Martensitic Wires, Preprint Laboratoire J. L. Lions, Univ. P. et M. Curie, Parigi, in preparation. | DOI | MR | Zbl
- ,[37] Multiple Integrals in the Calculus of Variations, Springer-Verlag Berlin, 1966. | MR | Zbl
,[38] Parametrized measures and Variational Principles, Birkhäuser, Boston (1997). | DOI | MR
,[39] Second Order Analysis for Thin Structures, Nonlinear Anal., Theory Methods Appl., 56A, n. 5 (2004), 679-713. | DOI | MR | Zbl
- ,[40] Heterogeneous Thin Films of Martensitic Materials, Arch. Rational Mech. Anal. 153, n. 1 (2000), 39-90. | DOI | MR | Zbl
,[41] Elastic Materials with Couple-Stresses, Arch. Rational Mech. Anal., 11, (1962), 386-414. | DOI | MR | Zbl
,[42] Theories of Elasticity with Couple Stress, Arch. Rational Mech. Anal., 17 (1964), 85-112. | DOI | MR | Zbl
,[43] A course on Young Measures, Rend. Ist. Mat. Univ. Trieste, 26, Suppl., (1994), 349-394. | MR
,