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A note on non lower semicontinuous perimeter functionals on partitions
1. | Westfälische-Wilhelms Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany |
2. | Dipartimento di Matematica, Universitá di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa |
References:
[1] |
L. Ambrosio and A. Braides, Functionals defined on partitions in sets of finite perimeter. II, J. Math. Pures Appl., 69 (1990), 307-333. |
[2] |
E. Bretin and S. Masnou, A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics, Preprint, 2015. |
[3] |
S. Esedoglu and F. Otto, Threshold dynamics for networks with arbitrary surface tensions, Comm. Pure Appl. Math., 68 (2015), 808-864.
doi: 10.1002/cpa.21527. |
[4] |
G. P. Leonardi, Infiltrations in immiscible fluids systems, Proc. Roy Soc. Edimburgh, 131 (2001), 425-436.
doi: 10.1017/S0308210500000937. |
[5] |
F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems, Cambridge studies in advanced mathematics, 2012.
doi: 10.1017/CBO9781139108133. |
[6] |
F. Morgan, Immiscible fluid clusters in $\mathbb R^2$ and $\mathbb R^3$, Michigan Math. J., 45 (1998), 441-450.
doi: 10.1307/mmj/1030132292. |
[7] |
M. Ritoré and E. Vernadakis, Isoperimetric inequalities in Euclidean convex bodies, Trans. Amer. Math. Soc., 367 (2015), 4983-5014.
doi: 10.1090/S0002-9947-2015-06197-2. |
[8] |
T. Schmidt, Strict interior approximation of sets of finite perimeter and functions of bounded variation, Proc. Am. Math. Soc., 143 (2015), 2069-2084.
doi: 10.1090/S0002-9939-2014-12381-1. |
[9] |
A. Voß-Böhme and A. Deutsch, The cellular basis of cell sorting kinetics, J. Theoret. Biol., 263 (2010), 419-436.
doi: 10.1016/j.jtbi.2009.12.011. |
[10] |
B. White, Existence of least-energy configurations of immiscible fluids, J. Geom. Analysis, 6 (1996), 151-161.
doi: 10.1007/BF02921571. |
show all references
References:
[1] |
L. Ambrosio and A. Braides, Functionals defined on partitions in sets of finite perimeter. II, J. Math. Pures Appl., 69 (1990), 307-333. |
[2] |
E. Bretin and S. Masnou, A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics, Preprint, 2015. |
[3] |
S. Esedoglu and F. Otto, Threshold dynamics for networks with arbitrary surface tensions, Comm. Pure Appl. Math., 68 (2015), 808-864.
doi: 10.1002/cpa.21527. |
[4] |
G. P. Leonardi, Infiltrations in immiscible fluids systems, Proc. Roy Soc. Edimburgh, 131 (2001), 425-436.
doi: 10.1017/S0308210500000937. |
[5] |
F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems, Cambridge studies in advanced mathematics, 2012.
doi: 10.1017/CBO9781139108133. |
[6] |
F. Morgan, Immiscible fluid clusters in $\mathbb R^2$ and $\mathbb R^3$, Michigan Math. J., 45 (1998), 441-450.
doi: 10.1307/mmj/1030132292. |
[7] |
M. Ritoré and E. Vernadakis, Isoperimetric inequalities in Euclidean convex bodies, Trans. Amer. Math. Soc., 367 (2015), 4983-5014.
doi: 10.1090/S0002-9947-2015-06197-2. |
[8] |
T. Schmidt, Strict interior approximation of sets of finite perimeter and functions of bounded variation, Proc. Am. Math. Soc., 143 (2015), 2069-2084.
doi: 10.1090/S0002-9939-2014-12381-1. |
[9] |
A. Voß-Böhme and A. Deutsch, The cellular basis of cell sorting kinetics, J. Theoret. Biol., 263 (2010), 419-436.
doi: 10.1016/j.jtbi.2009.12.011. |
[10] |
B. White, Existence of least-energy configurations of immiscible fluids, J. Geom. Analysis, 6 (1996), 151-161.
doi: 10.1007/BF02921571. |
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