Singular solutions of fractional order conformal laplacians

Journal of Geometric Analysis

Volumn 22, Issue 3, 2012, Pages 845-863

  González, Maria Del Mar ^a   Mazzeo, Rafe ^b   Sire, Yannick ^c  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b STANFORD UNIVERSITY   (United States)

^c AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Fractional conformal Laplacian; Q curvature; Yamabe problem

Indexed keywords

EID: 84863838727     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12220-011-9217-9     Document Type: Article

References (25)

1. Cabré, X., Sire, Y.: Nonlinear equations for fractional Laplacians I: Regularity, maximum principles and Hamiltonian estimates. Preprint arXiv:1012.0867
2. Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32(8), 1245 (2007)
3. Chang, A., Gonzalez, M.d.M.: Fractional Laplacian in conformal geometry. Adv. Math. 226(2), 1410-1432 (2011)
4. Chang, S.-Y.A., Hang, F., Yang, P.C.: On a class of locally conformally flat manifolds. Int. Math. Res. Not. 4, 185-209 (2004) (Pubitemid 38483016)
5. Chen, W., Li, C., Ou, B.: Classification of solutions for an integral equation. Commun. Pure Appl. Math. 59(3), 330-343 (2006)
6. Duistermaat, J.J., Hörmander, L.: Fourier integral operators. II. Acta Math. 128(3-4), 183-269 (1972)
7. Fabes, E.B., Kenig, C.E., Serapioni, R.P.: The local regularity of solutions of degenerate elliptic equations. Commun. Partial Differ. Equ. 7(1), 77-116 (1982)
8. p = 0 whose singular set is a manifold with boundary. Calc. Var. Partial Differ. Equ. 17(2), 179-197 (2003) (Pubitemid 36742921)
9. Gidas, B., Ni, W.M., Nirenberg, L.: Symmetry and related properties via the maximum principle. Commun. Math. Phys. 68(3), 209-243 (1979)
10. Gidas, B., Ni, W.M., Nirenberg, L.: Symmetry of positive solutions of nonlinear elliptic equations in Rn. In: Mathematical Analysis and Applications, Part A. Adv. in Math. Suppl. Stud., vol. 7, pp. 369-402. Academic Press, New York (1981)
11. González, M.d.M.: Singular sets of a class of locally conformally flatmanifolds. DukeMath. J. 129(3), 551-572 (2005)
12. González, M.d.M., Qing, J.: Fractional conformal Laplacians and fractional Yamabe problems. Preprint arXiv:1012.0579
13. Graham, C.R., Jenne, R., Mason, L.J., Sparling, G.A.J.: Conformally invariant powers of the Laplacian. I. Existence. J. Lond. Math. Soc. (2) 46(3), 557-565 (1992)
14. Graham, C.R., Zworski, M.: Scattering matrix in conformal geometry. Invent. Math. 152(1), 89-118 (2003) (Pubitemid 36754990)
15. Juhl, A.: Families of Conformally Covariant Differential Operators, Q-Curvature and Holography. Progress in Mathematics, vol. 275. Birkhäuser, Basel (2009)
16. Juhl, A.: On conformally covariant powers of the Laplacian. Preprint arXiv:0905.3992
17. Labutin, D.A.:Wiener regularity for large solutions of nonlinear equations. Ark. Mat. 41(2), 307-339 (2003) (Pubitemid 37347090)
18. Mazzeo, R.: Elliptic theory of differential edge operators I. Commun. Partial Differ. Equ. 16(10), 1615-1664 (1991)
19. Mazzeo, R., Pacard, F.: A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis. J. Differ. Geom. 44(2), 331-370 (1996) (Pubitemid 126312317)
20. Peterson, L.J.: Conformally covariant pseudo-differential operators. Differ. Geom. Appl. 13(2), 197-211 (2000)
21. Pollack, D.: Compactness results for complete metrics of constant positive scalar curvature on subdomains of Sn. Indiana Univ. Math. J. 42(4), 1441-1456 (1993)
22. Qing, J., Raske, D.: On positive solutions to semilinear conformally invariant equations on locally conformally flat manifolds. Int. Math. Res. Not. 20, 94172 (2006)
23. Reed, M., Simon, B.: Fourier Analysis, Self-Adjointness. Methods of Mathematical Physics, vol. 2. Academic Press, New York (1975)
24. Schoen, R.M.: On the number of constant scalar curvature metrics in a conformal class. In: Differential Geometry. Pitman Monogr. Surveys Pure Appl. Math., vol. 52, pp. 311-320. Longman Sci. Tech., Harlow (1991)
25. Schoen, R., Yau, S.-T.: Conformally flat manifolds, Kleinian groups and scalar curvature. Invent. Math. 92(1), 47-71 (1988)