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Volumn 258, Issue 2, 2010, Pages 458-503

Multiple-end solutions to the Allen-Cahn equation in R2

Author keywords

Allen Cahn equation; Infinite dimensional Lyapunov Schmidt reduction; Moduli spaces; Multiple end solutions; Toda system

Indexed keywords


EID: 70350591980     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2009.04.020     Document Type: Article
Times cited : (90)

References (26)
  • 1
    • 0030594276 scopus 로고    scopus 로고
    • Critical spectrum and stability of interfaces for a class of reaction-diffusion equations
    • Alikakos N., Fusco G., and Stefanopoulos V. Critical spectrum and stability of interfaces for a class of reaction-diffusion equations. J. Differential Equations 126 1 (1996) 106-167
    • (1996) J. Differential Equations , vol.126 , Issue.1 , pp. 106-167
    • Alikakos, N.1    Fusco, G.2    Stefanopoulos, V.3
  • 2
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • Allen S., and Cahn J.W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979) 1084-1095
    • (1979) Acta Metall. , vol.27 , pp. 1084-1095
    • Allen, S.1    Cahn, J.W.2
  • 4
    • 70350606574 scopus 로고    scopus 로고
    • 2 m, preprint, 2008, arXiv:0801.3379
    • 2 m, preprint, 2008, arXiv:0801.3379
  • 6
    • 70350577738 scopus 로고    scopus 로고
    • Moduli space theory for some class of solutions to the Allen-Cahn equation in the plane
    • preprint
    • M. del Pino, M. Kowalczyk, F. Pacard, Moduli space theory for some class of solutions to the Allen-Cahn equation in the plane, preprint, 2008
    • (2008)
    • del Pino, M.1    Kowalczyk, M.2    Pacard, F.3
  • 7
    • 70350598538 scopus 로고    scopus 로고
    • The Toda system and multiple-end solutions of autonomous planar elliptic problems
    • in press
    • M. del Pino, M. Kowalczyk, F. Pacard, J. Wei, The Toda system and multiple-end solutions of autonomous planar elliptic problems, Adv. Math. (2009), in press
    • (2009) Adv. Math
    • del Pino, M.1    Kowalczyk, M.2    Pacard, F.3    Wei, J.4
  • 8
    • 33751518021 scopus 로고    scopus 로고
    • Concentration on curves for nonlinear Schrödinger equations
    • del Pino M., Kowalczyk M., and Wei J. Concentration on curves for nonlinear Schrödinger equations. Comm. Pure Appl. Math. 70 (2007) 113-146
    • (2007) Comm. Pure Appl. Math. , vol.70 , pp. 113-146
    • del Pino, M.1    Kowalczyk, M.2    Wei, J.3
  • 9
    • 50249108359 scopus 로고    scopus 로고
    • The Toda system and clustering interfaces in the Allen-Cahn equation
    • del Pino M., Kowalczyk M., and Wei J. The Toda system and clustering interfaces in the Allen-Cahn equation. Arch. Ration. Mech. Anal. 190 (2008) 141-187
    • (2008) Arch. Ration. Mech. Anal. , vol.190 , pp. 141-187
    • del Pino, M.1    Kowalczyk, M.2    Wei, J.3
  • 10
    • 70350617314 scopus 로고    scopus 로고
    • A conjecture by de Giorgi in large dimensions
    • preprint
    • M. del Pino, M. Kowalczyk, J. Wei, A conjecture by de Giorgi in large dimensions, preprint, 2008
    • (2008)
    • del Pino, M.1    Kowalczyk, M.2    Wei, J.3
  • 11
    • 70350611760 scopus 로고    scopus 로고
    • Interface foliation on Riemannian manifolds with positive Ricci curvature
    • preprint
    • M. del Pino, M. Kowalczyk, J. Wei, J. Yang, Interface foliation on Riemannian manifolds with positive Ricci curvature, preprint, 2008
    • (2008)
    • del Pino, M.1    Kowalczyk, M.2    Wei, J.3    Yang, J.4
  • 12
    • 0001294525 scopus 로고    scopus 로고
    • N and related conjectures
    • N and related conjectures. Ric. Mat. 48 (1999) 129-154
    • (1999) Ric. Mat. , vol.48 , pp. 129-154
    • Farina, A.1
  • 13
    • 80051924152 scopus 로고    scopus 로고
    • The state of the art for a conjecture of De Giorgi and related problems
    • Ishii H., Lin W.-Y., and Du Y. (Eds), World Scientific
    • Farina A., and Valdinoci E. The state of the art for a conjecture of De Giorgi and related problems. In: Ishii H., Lin W.-Y., and Du Y. (Eds). Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions (2008), World Scientific
    • (2008) Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions
    • Farina, A.1    Valdinoci, E.2
  • 14
    • 0032373311 scopus 로고    scopus 로고
    • On a conjecture of de Giorgi and some related problems
    • Ghoussoub N., and Gui C. On a conjecture of de Giorgi and some related problems. Math. Ann. 311 (1998) 481-491
    • (1998) Math. Ann. , vol.311 , pp. 481-491
    • Ghoussoub, N.1    Gui, C.2
  • 15
    • 38049103351 scopus 로고    scopus 로고
    • Hamiltonian identities for elliptic partial differential equations
    • Gui C. Hamiltonian identities for elliptic partial differential equations. J. Funct. Anal. 254 4 (2008) 904-933
    • (2008) J. Funct. Anal. , vol.254 , Issue.4 , pp. 904-933
    • Gui, C.1
  • 16
    • 70350607387 scopus 로고    scopus 로고
    • Allen Cahn equation and its generalizations
    • preprint
    • C. Gui, Allen Cahn equation and its generalizations, preprint, 2008
    • (2008)
    • Gui, C.1
  • 17
    • 0010598327 scopus 로고    scopus 로고
    • Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory
    • Hutchinson J.E., and Tonegawa Y. Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory. Calc. Var. 10 (2000) 49-84
    • (2000) Calc. Var. , vol.10 , pp. 49-84
    • Hutchinson, J.E.1    Tonegawa, Y.2
  • 19
    • 0000876641 scopus 로고
    • The solution to a generalized Toda lattice and representation theory
    • Kostant B. The solution to a generalized Toda lattice and representation theory. Adv. Math. 34 (1979) 195-338
    • (1979) Adv. Math. , vol.34 , pp. 195-338
    • Kostant, B.1
  • 20
    • 24944545330 scopus 로고    scopus 로고
    • On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
    • Kowalczyk M. On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions. Ann. Mat. Pura Appl. (4) 184 1 (2005) 17-52
    • (2005) Ann. Mat. Pura Appl. (4) , vol.184 , Issue.1 , pp. 17-52
    • Kowalczyk, M.1
  • 21
    • 0036425683 scopus 로고    scopus 로고
    • Boundary concentration phenomena for a singularly perturbed elliptic problem
    • Malchiodi A., and Montenegro M. Boundary concentration phenomena for a singularly perturbed elliptic problem. Comm. Pure Appl. Math. 55 12 (2002) 1507-1568
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.12 , pp. 1507-1568
    • Malchiodi, A.1    Montenegro, M.2
  • 22
    • 4043167077 scopus 로고    scopus 로고
    • Multidimensional boundary layers for a singularly perturbed Neumann problem
    • Malchiodi A., and Montenegro M. Multidimensional boundary layers for a singularly perturbed Neumann problem. Duke Math. J. 124 1 (2004) 105-143
    • (2004) Duke Math. J. , vol.124 , Issue.1 , pp. 105-143
    • Malchiodi, A.1    Montenegro, M.2
  • 24
    • 0000641586 scopus 로고
    • Finitely many mass points on the line under the influence of an exponential potential - an integrable system
    • Dynamical Systems, Theory and Applications. Rencontres, Battelle Res. Inst., Seattle, Wash., 1974, Springer, Berlin
    • Moser J. Finitely many mass points on the line under the influence of an exponential potential - an integrable system. Dynamical Systems, Theory and Applications. Rencontres, Battelle Res. Inst., Seattle, Wash., 1974. Lecture Notes in Phys. vol. 38 (1975), Springer, Berlin 467-497
    • (1975) Lecture Notes in Phys. , vol.38 , pp. 467-497
    • Moser, J.1
  • 25
    • 2642588420 scopus 로고    scopus 로고
    • From the constant mean curvature hypersurfaces to the gradient theory of phase transitions
    • Pacard F., and Ritoré M. From the constant mean curvature hypersurfaces to the gradient theory of phase transitions. J. Differential Geom. 64 3 (2003) 356-423
    • (2003) J. Differential Geom. , vol.64 , Issue.3 , pp. 356-423
    • Pacard, F.1    Ritoré, M.2
  • 26
    • 67249165287 scopus 로고    scopus 로고
    • Regularity of flat level sets in phase transitions
    • Savin O. Regularity of flat level sets in phase transitions. Ann. of Math. (2) 169 1 (2009) 47-78
    • (2009) Ann. of Math. (2) , vol.169 , Issue.1 , pp. 47-78
    • Savin, O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.