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Fracture models as $\Gamma$-limits of damage models
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References:
[1] |
G. Alberti, G. Bouchitté and P. Seppecher, Phase transition with line-tension effect, Arch. Rational Mech. Anal., 144 (1998), 1-46.
doi: 10.1007/s002050050111. |
[2] |
F. J. Almgren and E. H. Lieb, Symmetric decreasing rearrangement is sometimes continuous, J. Amer. Math. Soc., 2 (1989), 683-773.
doi: 10.2307/1990893. |
[3] |
L. Ambrosio, L. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems," Oxford University Press, Oxford, 2000. |
[4] |
L. Ambrosio, A. Lemenant and G. Royer-Carfagni, A variational model for plastic slip and its regularization via $\Gamma$-convergence,, J. Elasticity, (): 10659.
doi: 10.1007/s10659-012-9390-5. |
[5] |
L. Ambrosio and V. M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via $\Gamma$-convergence, Comm. Pure Appl. Math., 43 (1990), 999-1036.
doi: 10.1002/cpa.3160430805. |
[6] |
L. Ambrosio and V. M. Tortorelli, On the approximation of free discontinuity problems, Boll. Un. Mat. Ital., 6-B (1992), 105-123. |
[7] |
B. Bourdin, G. A. Francfort and J.-J. Marigo, The variational approach to fracture, J. Elasticity, 91 (2008), 5-148.
doi: 10.1007/s10659-007-9107-3. |
[8] |
G. Buttazzo, "Semicontinuity, Relaxation and Integral Representation in the Calculus of Variation," Pitman Res. Notes Math. Ser., 203, Longman, Harlow, 1989. |
[9] |
J.-M. Coron, The continuity of the rearrangement in $W^{1,p}(R)$, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 11 (1984), 57-85. |
[10] |
G. Cortesani and R. Toader, A density result in SBV with respect to non-isotropic energies, Nonlinear Anal., 38 (1999), 585-604.
doi: 10.1016/S0362-546X(98)00132-1. |
[11] |
G. Dal Maso, "An Introduction to $\Gamma$-Convergence," Birkhäuser, Basel, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[12] |
L. C. Evans and R. F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992. |
[13] |
H. Federer, "Geometric Measure Theory," Springer-Verlag, 1969. |
[14] |
E. Giusti, "Minimal Surfaces and Functions of Bounded Variation," Monographs in Mathematics 80, Birkhäuser, Basel, 1984. |
[15] |
K. Hilden, Symmetrization of functions in Sobolev spaces and the isoperimetric inequality, Manuscripta Math., 18 (1976), 215-235. |
[16] |
F. Iurlano, Fracture and plastic models as $\Gamma$-limits of damage models under different regimes,, Adv. Calc. Var., ().
|
[17] |
G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 110 (1976), 353-372. |
show all references
References:
[1] |
G. Alberti, G. Bouchitté and P. Seppecher, Phase transition with line-tension effect, Arch. Rational Mech. Anal., 144 (1998), 1-46.
doi: 10.1007/s002050050111. |
[2] |
F. J. Almgren and E. H. Lieb, Symmetric decreasing rearrangement is sometimes continuous, J. Amer. Math. Soc., 2 (1989), 683-773.
doi: 10.2307/1990893. |
[3] |
L. Ambrosio, L. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems," Oxford University Press, Oxford, 2000. |
[4] |
L. Ambrosio, A. Lemenant and G. Royer-Carfagni, A variational model for plastic slip and its regularization via $\Gamma$-convergence,, J. Elasticity, (): 10659.
doi: 10.1007/s10659-012-9390-5. |
[5] |
L. Ambrosio and V. M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via $\Gamma$-convergence, Comm. Pure Appl. Math., 43 (1990), 999-1036.
doi: 10.1002/cpa.3160430805. |
[6] |
L. Ambrosio and V. M. Tortorelli, On the approximation of free discontinuity problems, Boll. Un. Mat. Ital., 6-B (1992), 105-123. |
[7] |
B. Bourdin, G. A. Francfort and J.-J. Marigo, The variational approach to fracture, J. Elasticity, 91 (2008), 5-148.
doi: 10.1007/s10659-007-9107-3. |
[8] |
G. Buttazzo, "Semicontinuity, Relaxation and Integral Representation in the Calculus of Variation," Pitman Res. Notes Math. Ser., 203, Longman, Harlow, 1989. |
[9] |
J.-M. Coron, The continuity of the rearrangement in $W^{1,p}(R)$, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 11 (1984), 57-85. |
[10] |
G. Cortesani and R. Toader, A density result in SBV with respect to non-isotropic energies, Nonlinear Anal., 38 (1999), 585-604.
doi: 10.1016/S0362-546X(98)00132-1. |
[11] |
G. Dal Maso, "An Introduction to $\Gamma$-Convergence," Birkhäuser, Basel, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[12] |
L. C. Evans and R. F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992. |
[13] |
H. Federer, "Geometric Measure Theory," Springer-Verlag, 1969. |
[14] |
E. Giusti, "Minimal Surfaces and Functions of Bounded Variation," Monographs in Mathematics 80, Birkhäuser, Basel, 1984. |
[15] |
K. Hilden, Symmetrization of functions in Sobolev spaces and the isoperimetric inequality, Manuscripta Math., 18 (1976), 215-235. |
[16] |
F. Iurlano, Fracture and plastic models as $\Gamma$-limits of damage models under different regimes,, Adv. Calc. Var., ().
|
[17] |
G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 110 (1976), 353-372. |
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