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Some symmetry results for entire solutions of an elliptic system arising in phase separation
1. | LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France |
References:
[1] |
H. Berestycki, T.-C. Lin, J. Wei and C. Zhao, On phase-separation model: Asymptotics and qualitative properties, Arch. Ration. Mech. Anal., 208 (2013), 163-200.
doi: 10.1007/s00205-012-0595-3. |
[2] |
H. Berestycki, S. Terracini, K. Wang and J. Wei, On entire solutions of an elliptic system modeling phase separation, Adv. Math., 243 (2013), 102-126.
doi: 10.1016/j.aim.2013.04.012. |
[3] |
E. De Giorgi, Convergence problems for functionals and operators, in Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), Pitagora, Bologna, 1979, 131-188. |
[4] |
A. Farina and E. Valdinoci, The state of the art for a conjecture of De Giorgi and related problems, in Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions, World Scientific Publishers, Hackensack, NJ, 2009, 74-96.
doi: 10.1142/9789812834744_0004. |
[5] |
B. Noris, H. Tavares, S. Terracini and G. Verzini, Uniform Holder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302. |
show all references
References:
[1] |
H. Berestycki, T.-C. Lin, J. Wei and C. Zhao, On phase-separation model: Asymptotics and qualitative properties, Arch. Ration. Mech. Anal., 208 (2013), 163-200.
doi: 10.1007/s00205-012-0595-3. |
[2] |
H. Berestycki, S. Terracini, K. Wang and J. Wei, On entire solutions of an elliptic system modeling phase separation, Adv. Math., 243 (2013), 102-126.
doi: 10.1016/j.aim.2013.04.012. |
[3] |
E. De Giorgi, Convergence problems for functionals and operators, in Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), Pitagora, Bologna, 1979, 131-188. |
[4] |
A. Farina and E. Valdinoci, The state of the art for a conjecture of De Giorgi and related problems, in Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions, World Scientific Publishers, Hackensack, NJ, 2009, 74-96.
doi: 10.1142/9789812834744_0004. |
[5] |
B. Noris, H. Tavares, S. Terracini and G. Verzini, Uniform Holder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302. |
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