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1. | SISSA - International School for Advanced Studies, Sector of Mathematical Analysis Via Bonomea, 265, 34136 Trieste |
  Our setting is very general, and it comprises, as a particular case, a conjecture of De Giorgi for phase separations in $\mathbb{R}^2$.
References:
[1] |
H. Berestycki, T.-C. Lin, J. Wei and C. Zhao, On phase-separation model: Asymptotics and qualitative properties,, preprint., ().
|
[2] |
H. Berestycki, S. Terracini, K. Wang and J. Wei, Existence and stability of entire solutions of an elliptic system modeling phase separation,, preprint., ().
|
[3] |
S. Dipierro and A. Pinamonti, A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian,, preprint., ().
|
[4] |
L. C. Evans and R. F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. |
[5] |
A. Farina, "Propriétés Qualitatives de Solutions d'Équations et Systèmes d'Équations Non-Linéaires," Habilitation à Diriger des Recherches, Paris VI, 2002. |
[6] |
A. Farina, B. Sciunzi and E. Valdinoci, Bernstein and De Giorgi type problems: New results via a geometric approach, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 7 (2008), 741-791. |
[7] |
A. Farina and E. Valdinoci, The state of the art for a conjecture of De Giorgi and related problems. Recent progress on reaction-diffusion systems and viscosity solutions, in "Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions," World Sci. Publ., Hackensack, NJ, (2009), 74-96.
doi: 10.1142/9789812834744_0004. |
[8] |
M. Fazly and N. Ghoussoub, De Giorgi type results for elliptic systems,, Calc. Var. and PDE., ().
|
[9] |
B. Noris, H. Tavares, S. Terracini and G. Verzin, Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302. |
[10] |
E. H. Lieb and M. Loss, "Analysis," Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997. |
[11] |
E. Sernesi, "Geometria 2," Bollati Boringhieri, Torino, 1994. |
[12] |
P. Sternberg and K. Zumbrun, Connectivity of phase boundaries in strictly convex domains, Arch. Rational Mech. Anal., 141 (1998), 375-400.
doi: 10.1007/s002050050081. |
[13] |
P. Sternberg and K. Zumbrun, A Poincaré inequality with applications to volume-constrained area-minimizing surfaces, J. Reine Angew. Math., 503 (1998), 63-85. |
[14] |
K. Wang, On the De Giorgi type conjecture for an elliptic system modeling phase separation,, preprint., ().
|
show all references
References:
[1] |
H. Berestycki, T.-C. Lin, J. Wei and C. Zhao, On phase-separation model: Asymptotics and qualitative properties,, preprint., ().
|
[2] |
H. Berestycki, S. Terracini, K. Wang and J. Wei, Existence and stability of entire solutions of an elliptic system modeling phase separation,, preprint., ().
|
[3] |
S. Dipierro and A. Pinamonti, A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian,, preprint., ().
|
[4] |
L. C. Evans and R. F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. |
[5] |
A. Farina, "Propriétés Qualitatives de Solutions d'Équations et Systèmes d'Équations Non-Linéaires," Habilitation à Diriger des Recherches, Paris VI, 2002. |
[6] |
A. Farina, B. Sciunzi and E. Valdinoci, Bernstein and De Giorgi type problems: New results via a geometric approach, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 7 (2008), 741-791. |
[7] |
A. Farina and E. Valdinoci, The state of the art for a conjecture of De Giorgi and related problems. Recent progress on reaction-diffusion systems and viscosity solutions, in "Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions," World Sci. Publ., Hackensack, NJ, (2009), 74-96.
doi: 10.1142/9789812834744_0004. |
[8] |
M. Fazly and N. Ghoussoub, De Giorgi type results for elliptic systems,, Calc. Var. and PDE., ().
|
[9] |
B. Noris, H. Tavares, S. Terracini and G. Verzin, Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302. |
[10] |
E. H. Lieb and M. Loss, "Analysis," Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997. |
[11] |
E. Sernesi, "Geometria 2," Bollati Boringhieri, Torino, 1994. |
[12] |
P. Sternberg and K. Zumbrun, Connectivity of phase boundaries in strictly convex domains, Arch. Rational Mech. Anal., 141 (1998), 375-400.
doi: 10.1007/s002050050081. |
[13] |
P. Sternberg and K. Zumbrun, A Poincaré inequality with applications to volume-constrained area-minimizing surfaces, J. Reine Angew. Math., 503 (1998), 63-85. |
[14] |
K. Wang, On the De Giorgi type conjecture for an elliptic system modeling phase separation,, preprint., ().
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