Liouville type theorems for some conformally invariant fully nonlinear equations

YanYan Li

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2003)

  • Volume: 14, Issue: 3, page 219-225
  • ISSN: 1120-6330

Abstract

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This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.

How to cite

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Li, YanYan. "Liouville type theorems for some conformally invariant fully nonlinear equations." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.3 (2003): 219-225. <http://eudml.org/doc/252446>.

@article{Li2003,
abstract = {This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.},
author = {Li, YanYan},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Liouville type theorems; Conformally invariant equations; conformally invariant equations},
language = {eng},
month = {9},
number = {3},
pages = {219-225},
publisher = {Accademia Nazionale dei Lincei},
title = {Liouville type theorems for some conformally invariant fully nonlinear equations},
url = {http://eudml.org/doc/252446},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Li, YanYan
TI - Liouville type theorems for some conformally invariant fully nonlinear equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/9//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 3
SP - 219
EP - 225
AB - This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.
LA - eng
KW - Liouville type theorems; Conformally invariant equations; conformally invariant equations
UR - http://eudml.org/doc/252446
ER -

References

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  1. CAFFARELLI, L. - GIDAS, B. - SPRUCK, J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math., 42, 1989, 271-297. Zbl0702.35085MR982351DOI10.1002/cpa.3160420304
  2. CAFFARELLI, L. - NIRENBERG, L. - SPRUCK, J., The Dirichlet problem for nonlinear second-order elliptic equations, III: Functions of the eigenvalues of the Hessian. Acta Math., 155, 1985, 261-301. Zbl0654.35031MR806416DOI10.1007/BF02392544
  3. CHANG, S.Y. A. - GURSKY, M. - YANG, P., An a priori estimate for a fully nonlinear equation on four-manifolds. Preprint. Zbl1067.58028
  4. CHANG, S.Y. A. - GURSKY, M. - YANG, P., Entire solutions of a fully nonlinear equation. Preprint. Zbl1183.53035MR2055838
  5. CHEN, W. - LI, C., Classification of solutions of some nonlinear elliptic equations. Duke Math. J., 63, 1991, 615-622. Zbl0768.35025MR1121147DOI10.1215/S0012-7094-91-06325-8
  6. GIDAS, B. - NI, W.M. - NIRENBERG, L., Symmetry and related properties via the maximum principle. Comm. Math. Phys., 68, 1979, 209-243. Zbl0425.35020MR544879
  7. GIDAS, B. - SPRUCK, J., Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math., 34, 1981, 525-598. Zbl0465.35003MR615628DOI10.1002/cpa.3160340406
  8. LI, A. - LI, Y.Y., On some conformally invariant fully nonlinear equations. C. R. Acad. Sci. Paris, Ser. I, 334, 2002, 1-6. Zbl0998.58011MR1957529
  9. LI, A. - LI, Y.Y., On some conformally invariant fully nonlinear equations. Comm. Pure Appl. Math., to appear. Zbl1155.35353MR2706075
  10. LI, A. - LI, Y.Y., A general Liouville type theorem for some conformally invariant fully nonlinear equations. arXiv:math.AP/0301239 v1 21 Jan 2003. Zbl1221.35149
  11. LI, A. - LI, Y.Y., Further results on Liouville type theorems for some conformally invariant fully nonlinear equations. arXiv:math.AP/0301254 v1 22 Jan 2003. Zbl1221.35149
  12. LI, A. - LI, Y.Y., On some conformally invariant fully nonlinear equations, Part II: Liouville, Harnack and Yamabe. In preparation. Zbl1216.35038
  13. LI, Y.Y. - ZHANG, L., Liouville type theorems and Harnack type inequalities for semilinear elliptic equations. Journal d’Analyse Mathematique, to appear. Zbl1173.35477MR2001065DOI10.1007/BF02786551
  14. LI, Y.Y. - ZHU, M., Uniqueness theorems through the method of moving spheres. Duke Math. J., 80, 1995, 383-417. Zbl0846.35050MR1369398DOI10.1215/S0012-7094-95-08016-8
  15. OBATA, M., The conjecture on conformal transformations of Riemannian manifolds. J. Diff. Geom., 6, 1971, 247-258. Zbl0236.53042MR303464
  16. VIACLOVSKY, J., Conformal geometry, contact geometry, and the calculus of variations. Duke Math. J., 101, 2000, 283-316. Zbl0990.53035MR1738176DOI10.1215/S0012-7094-00-10127-5
  17. VIACLOVSKY, J., Conformally invariant Monge-Ampere equations: global solutions. Trans. Amer. Math. Soc., 352, 2000, 4371-4379. Zbl0951.35044MR1694380DOI10.1090/S0002-9947-00-02548-4

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