Relaxation of certain integral functionals depending on strain and chemical composition

Ana Margarida Ribeiro , Elvira Zappale

Chinese Annals of Mathematics, Series B ›› 2013, Vol. 34 ›› Issue (4) : 491 -514.

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Chinese Annals of Mathematics, Series B ›› 2013, Vol. 34 ›› Issue (4) : 491 -514. DOI: 10.1007/s11401-013-0784-x
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Relaxation of certain integral functionals depending on strain and chemical composition

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Abstract

The authors provide a relaxation result in BV × L q, 1 ≤ q < + ∞ as the first step towards the analysis of thermochemical equilibria.

Keywords

Relaxation / Functions of bounded variation / Quasiconvexity

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Ana Margarida Ribeiro, Elvira Zappale. Relaxation of certain integral functionals depending on strain and chemical composition. Chinese Annals of Mathematics, Series B, 2013, 34(4): 491-514 DOI:10.1007/s11401-013-0784-x

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References

[1]

Ambrosio L, Maso G D. On the relaxation in BV (Ω; ℝm) of quasi-convex integrals. J. Funct. Anal., 1992, 109: 76-97

[2]

Ambrosio L, Fusco N, Pallara D. Functions of Bounded Variation and Free Discontinuity Problems, 2000, Oxford: Clarendon Press

[3]

Ambrosio L, Mortola S, Tortorelli V M. Functionals with linear growth defined on vector valued BV functions. J. Math. Pures Appl., 1991, 70(3): 269-323

[4]

Aujol J F, Aubert G, Blanc-Féraud L, Chambolle A. Image decomposition into a bounded variation component and an oscillating component. J. Math. Imaging and Vision, 2005, 22(1): 71-88

[5]

Aujol J F, Aubert G, Blanc-Féraud L, Chambolle A. Decomposing an image: Application to SAR images, Scale-Space’ 03, 2003 297-312

[6]

Aujol J F, Kang S H. Color image decomposition and restoration. J. Visual Commun. and Image Representation, 2006, 17(4): 916-928

[7]

Babadjian J F, Zappale E, Zorgati H. Dimensional reduction for energies with linear growth involving the bending moment. J. Math. Pures Appl. (9), 2008, 90(6): 520-549

[8]

Braides A, Fonseca I, Leoni G. A-quasiconvexity: relaxation and homogenization. ESAIM: Control, Optimization and Calculus of Variations, 2000, 5: 539-577

[9]

Carita G, Ribeiro A M, Zappale E. An homogenization result in W 1,p × L q. J. Convex Anal., 2011, 18(4): 1093-1126

[10]

Carita G, Ribeiro A M, Zappale E. Relaxation for some integral functionals in W w 1,p×L w q. Bol. Soc. Port. Mat., Special Issue, 2010 47-53

[11]

Dacorogna B. Direct Methods in the Calculus of Variations, 2008 2nd ed. Berlin: Springer-Verlag

[12]

Dal Maso G, Fonseca I, Leoni G, Morini M. Higher order quasiconvexity reduces to quasiconvexity. Arch. Rational Mech. Anal., 2004, 171(51): 55-81

[13]

Ekeland I, Temam R. Convex analysis and variational problems, 1976, Amsterdam, Oxford: North-Holland Publishing Company

[14]

Fonseca I, Kinderlehrer D, Pedregal P. Relaxation in BV × L of functionals depending on strain and composition, Boundary Value Problems for Partial Differential Equations and Applications (Dedicated to Enrico Magenes on the occasion of his 70th birthday), J. L. Lions, et al. (eds.). Masson. Res. Notes Appl. Math., 1993, 29: 113-152

[15]

Fonseca I, Kinderlehrer D, Pedregal P. Energy functionals depending on elastic strain and chemical composition. Calc. Var. Part. Diff. Eq., 1994, 2: 283-313

[16]

Fonseca I, Leoni G. Modern Methods in the Calculus of Variations: L p Spaces, 2007, New York: Springer-Verlag

[17]

Fonseca I, Müller S. Relaxation of quasiconvex functionals in BV (Ω; ℝp) for integrands f(x, u,∇u). Arch. Rational Mech. Anal., 1993, 123: 1-49

[18]

Fonseca I, Rybka P. Relaxation of multiple integrals in the space BV (Ω, ℝp). Proc. R. Soc. Edinb., Sect. A, 1992, 121(3–4): 321-348

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