메뉴 건너뛰기




Volumn 346, Issue 23-24, 2008, Pages 1261-1266

A counterexample to a conjecture by De Giorgi in large dimensions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 57049180714     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2008.10.010     Document Type: Article
Times cited : (27)

References (23)
  • 1
    • 0034957494 scopus 로고    scopus 로고
    • On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property
    • Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday
    • Alberti G., Ambrosio L., and Cabré X. On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property. Acta Appl. Math. 65 1-3 (2001) 9-33 Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday
    • (2001) Acta Appl. Math. , vol.65 , Issue.1-3 , pp. 9-33
    • Alberti, G.1    Ambrosio, L.2    Cabré, X.3
  • 3
    • 0034412523 scopus 로고    scopus 로고
    • The Liouville property and a conjecture of De Giorgi
    • Barlow M.T., Bass R.F., and Gui C. The Liouville property and a conjecture of De Giorgi. Comm. Pure Appl. Math. 53 8 (2000) 1007-1038
    • (2000) Comm. Pure Appl. Math. , vol.53 , Issue.8 , pp. 1007-1038
    • Barlow, M.T.1    Bass, R.F.2    Gui, C.3
  • 4
    • 0001287814 scopus 로고    scopus 로고
    • One-dimensional symmetry of bounded entire solutions of some elliptic equations
    • Berestycki H., Hamel F., and Monneau R. One-dimensional symmetry of bounded entire solutions of some elliptic equations. Duke Math. J. 103 (2000) 375-396
    • (2000) Duke Math. J. , vol.103 , pp. 375-396
    • Berestycki, H.1    Hamel, F.2    Monneau, R.3
  • 5
  • 6
    • 57049127742 scopus 로고    scopus 로고
    • 2 m, Preprint, 2008
    • 2 m, Preprint, 2008
  • 7
    • 33646697141 scopus 로고    scopus 로고
    • Phase transitions: uniform regularity of the intermediate layers
    • Caffarelli L.A., and Cordoba A. Phase transitions: uniform regularity of the intermediate layers. J. Reine Angew. Math. 593 (2006) 209-235
    • (2006) J. Reine Angew. Math. , vol.593 , pp. 209-235
    • Caffarelli, L.A.1    Cordoba, A.2
  • 9
    • 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. 60 1 (2007) 113-146
    • (2007) Comm. Pure Appl. Math. , vol.60 , Issue.1 , pp. 113-146
    • del Pino, M.1    Kowalczyk, M.2    Wei, J.3
  • 10
    • 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. Rational Mech. Anal. 190 (2008) 141-187
    • (2008) Arch. Rational Mech. Anal. , vol.190 , pp. 141-187
    • del Pino, M.1    Kowalczyk, M.2    Wei, J.3
  • 11
    • 57049109958 scopus 로고    scopus 로고
    • M. del Pino, M. Kowalczyk, F. Pacard, J. Wei, The Toda system and multiple-end solutions of autonomous planar elliptic problems, Preprint, 2007
    • M. del Pino, M. Kowalczyk, F. Pacard, J. Wei, The Toda system and multiple-end solutions of autonomous planar elliptic problems, Preprint, 2007
  • 12
    • 57049128881 scopus 로고    scopus 로고
    • M. del Pino, M. Kowalczyk, J. Wei, On De Giorgi conjecture in dimension N ≥ 9, Preprint, 2008
    • M. del Pino, M. Kowalczyk, J. Wei, On De Giorgi conjecture in dimension N ≥ 9, Preprint, 2008
  • 13
    • 0001294525 scopus 로고    scopus 로고
    • N and related conjectures
    • N and related conjectures. Ricerche Mat. 48 suppl. (1999) 129-154
    • (1999) Ricerche Mat. , vol.48 , Issue.SUPPL , pp. 129-154
    • Farina, A.1
  • 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
    • 33746362550 scopus 로고    scopus 로고
    • Towards a counter-example to a conjecture of De Giorgi in high dimensions
    • Jerison D., and Monneau R. Towards a counter-example to a conjecture of De Giorgi in high dimensions. Ann. Mat. Pura Appl. 183 (2004) 439-467
    • (2004) Ann. Mat. Pura Appl. , vol.183 , pp. 439-467
    • Jerison, D.1    Monneau, R.2
  • 18
    • 34250109116 scopus 로고
    • The gradient theory of phase transitions and the minimal interface criterion
    • Modica L. The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 2 (1987) 123-142
    • (1987) Arch. Rational Mech. Anal. , vol.98 , Issue.2 , pp. 123-142
    • Modica, L.1
  • 20
    • 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
  • 21
    • 57049142191 scopus 로고    scopus 로고
    • O. Savin, Regularity of flat level sets in phase transitions, Ann. of Math., in press
    • O. Savin, Regularity of flat level sets in phase transitions, Ann. of Math., in press
  • 22
    • 84972535455 scopus 로고
    • Entire solutions of the minimal surface equation
    • Simon L. Entire solutions of the minimal surface equation. J. Differential Geometry 30 (1989) 643-688
    • (1989) J. Differential Geometry , vol.30 , pp. 643-688
    • Simon, L.1
  • 23
    • 0002460686 scopus 로고
    • Minimal varieties in riemannian manifolds
    • Simons J. Minimal varieties in riemannian manifolds. Ann. of Math. (2) 88 (1968) 62-105
    • (1968) Ann. of Math. (2) , vol.88 , pp. 62-105
    • Simons, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.