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On the $\Gamma$-limit for a non-uniformly bounded sequence of two-phase metric functionals
1. | Department of Mathematical Sciences, The University of Bath, Bath, BA2 7AY, United Kingdom, United Kingdom |
2. | Department of Mathematical Sciences, University of Bath, Bath BA2 7AY |
References:
[1] |
E. Acerbi and G. Buttazzo, On the limits of periodic Riemannian metrics,, J. Analyse Math., 43 (): 183.
doi: 10.1007/BF02790183. |
[2] |
M. Amar, G. Crasta and A. Malusa, On the Finsler metric obtained as limits of chessboard structures, Adv. Calc. Var., 2 (2009), 321-360.
doi: 10.1515/ACV.2009.013. |
[3] |
M. Amar and E. Vitali, Homogenization of periodic Finsler metrics, J. Convex Anal., 5 (1998), 171-186. |
[4] |
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, 1997.
doi: 10.1007/978-1-4757-2063-1. |
[5] |
A. Banerjee and N. Adams, Dynamics of classical systems based on the principle of stationary action,, J. Chem. Phys., 92 (): 7330.
doi: 10.1063/1.458218. |
[6] |
A. Braides, Almost periodic methods in the theory of homogenization, Appl. Anal., 47 (1992), 259-277.
doi: 10.1080/00036819208840144. |
[7] |
A. Braides, $\Gamma$-convergence for Beginners, Oxford University Press, 2002.
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[8] |
A. Braides, G. Buttazzo and I. Fragalá, Riemannian approximation of Finsler metrics, Asymptotic Analysis, 31 (2002), 177-187. |
[9] |
A. Braides and A. Defranceschi, Homogenisation of Multiple Integrals, Oxford University Press, 1998. |
[10] |
D. Burago, Y. Burago and S. Ivanov, A course in Metric Geometry, American Mathematical Society, 2001. |
[11] |
G. Buttazzo, L. D. Pascale and I. Fragalá, Topological equivalence of some variational problems involving distances, Discrete and Continuous Dynamical Systems, 7 (2001), 247-258.
doi: 10.3934/dcds.2001.7.247. |
[12] |
M. C. Concordel, Periodic homogenisation of Hamilton-Jacobi equations. II. Eikonal equations, Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 665-689.
doi: 10.1017/S0308210500023763. |
[13] |
B. Craciun and K. Bhattacharya, Homogenisation of a Hamilton-Jacobi equation associated with the geometric motion of an interface, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), 773-805.
doi: 10.1017/S0308210500002675. |
[14] |
W. E, A class of homogenisation problems in the calculus of variations, Comm. Pure Appl. Math., 44 (1991), 733-759.
doi: 10.1002/cpa.3160440702. |
[15] |
J. Jost, Riemannian Geometry and Geometric Analysis, 4th edition, Universitext, Springer-Verlag, Berlin, 2005. |
[16] |
P.-L. Lions, G. Papanicolaou and S. R. S. Varadhan, Homogenisation of Hamilton-Jacobi equations, preprint, 1988. |
[17] |
J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Springer-Verlag, New York, 1999.
doi: 10.1007/978-0-387-21792-5. |
[18] |
A. Oberman, R. Takei and A. Vladimirsky, Homogenisation of metric Hamilton-Jacobi equations, Multiscale Model. Simul., 8 (2009), 269-295.
doi: 10.1137/080743019. |
[19] |
H. Schwetlick, D. C. Sutton and J. Zimmer, The Finsler metric obtained as the $\Gamma$-limit of a generalised Manhattan metric,, to appear in J. Convex Anal., ().
|
[20] |
H. Schwetlick and J. Zimmer, Calculation of long time classical trajectories: Algorithmic treatment and applications for molecular systems, J. Chem. Phys., 130 (2009), 124106.
doi: 10.1063/1.3096294. |
[21] |
D. C. Sutton, Macroscopic Hamiltonian Systems and Their Effective Description, Ph.D thesis, University of Bath, 2013. |
show all references
References:
[1] |
E. Acerbi and G. Buttazzo, On the limits of periodic Riemannian metrics,, J. Analyse Math., 43 (): 183.
doi: 10.1007/BF02790183. |
[2] |
M. Amar, G. Crasta and A. Malusa, On the Finsler metric obtained as limits of chessboard structures, Adv. Calc. Var., 2 (2009), 321-360.
doi: 10.1515/ACV.2009.013. |
[3] |
M. Amar and E. Vitali, Homogenization of periodic Finsler metrics, J. Convex Anal., 5 (1998), 171-186. |
[4] |
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, 1997.
doi: 10.1007/978-1-4757-2063-1. |
[5] |
A. Banerjee and N. Adams, Dynamics of classical systems based on the principle of stationary action,, J. Chem. Phys., 92 (): 7330.
doi: 10.1063/1.458218. |
[6] |
A. Braides, Almost periodic methods in the theory of homogenization, Appl. Anal., 47 (1992), 259-277.
doi: 10.1080/00036819208840144. |
[7] |
A. Braides, $\Gamma$-convergence for Beginners, Oxford University Press, 2002.
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[8] |
A. Braides, G. Buttazzo and I. Fragalá, Riemannian approximation of Finsler metrics, Asymptotic Analysis, 31 (2002), 177-187. |
[9] |
A. Braides and A. Defranceschi, Homogenisation of Multiple Integrals, Oxford University Press, 1998. |
[10] |
D. Burago, Y. Burago and S. Ivanov, A course in Metric Geometry, American Mathematical Society, 2001. |
[11] |
G. Buttazzo, L. D. Pascale and I. Fragalá, Topological equivalence of some variational problems involving distances, Discrete and Continuous Dynamical Systems, 7 (2001), 247-258.
doi: 10.3934/dcds.2001.7.247. |
[12] |
M. C. Concordel, Periodic homogenisation of Hamilton-Jacobi equations. II. Eikonal equations, Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 665-689.
doi: 10.1017/S0308210500023763. |
[13] |
B. Craciun and K. Bhattacharya, Homogenisation of a Hamilton-Jacobi equation associated with the geometric motion of an interface, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), 773-805.
doi: 10.1017/S0308210500002675. |
[14] |
W. E, A class of homogenisation problems in the calculus of variations, Comm. Pure Appl. Math., 44 (1991), 733-759.
doi: 10.1002/cpa.3160440702. |
[15] |
J. Jost, Riemannian Geometry and Geometric Analysis, 4th edition, Universitext, Springer-Verlag, Berlin, 2005. |
[16] |
P.-L. Lions, G. Papanicolaou and S. R. S. Varadhan, Homogenisation of Hamilton-Jacobi equations, preprint, 1988. |
[17] |
J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Springer-Verlag, New York, 1999.
doi: 10.1007/978-0-387-21792-5. |
[18] |
A. Oberman, R. Takei and A. Vladimirsky, Homogenisation of metric Hamilton-Jacobi equations, Multiscale Model. Simul., 8 (2009), 269-295.
doi: 10.1137/080743019. |
[19] |
H. Schwetlick, D. C. Sutton and J. Zimmer, The Finsler metric obtained as the $\Gamma$-limit of a generalised Manhattan metric,, to appear in J. Convex Anal., ().
|
[20] |
H. Schwetlick and J. Zimmer, Calculation of long time classical trajectories: Algorithmic treatment and applications for molecular systems, J. Chem. Phys., 130 (2009), 124106.
doi: 10.1063/1.3096294. |
[21] |
D. C. Sutton, Macroscopic Hamiltonian Systems and Their Effective Description, Ph.D thesis, University of Bath, 2013. |
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