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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Homogeneous solutions to fully nonlinear elliptic equations


Authors: Nikolai Nadirashvili and Yu Yuan
Journal: Proc. Amer. Math. Soc. 134 (2006), 1647-1649
MSC (2000): Primary 35J60
Posted: January 17, 2006
MathSciNet review: 2204275
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Abstract | References | Similar Articles | Additional Information

Abstract: We classify homogeneous degree $ d\neq2$ solutions to fully nonlinear elliptic equations.

References

  • [CC] Caffarelli, L. A. and Cabré, X., Fully nonlinear elliptic equations. American Mathematical Society Colloquium Publications, 43, American Mathematical Society, Providence, RI, 1995. MR 1351007 (96h:35046)
  • [E] Evans, L. C., Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), 333-363. MR 0649348 (83g:35038)
  • [HNY] Han, Q., Nadirashvili, N., and Yuan, Yu, Linearity of homogeneous order-one solutions to elliptic equations in dimension three, Comm. Pure Appl. Math. 56 (2003), 425-432. MR 1949137 (2003k:35043)
  • [HL] Harvey, R. and Lawson, H. B. Jr., Calibrated geometry, Acta Math. 148 (1982), 47-157. MR 0666108 (85i:53058)
  • [K] Krylov, N. V., Boundedly nonhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 487-523 in Russian; English translation in Math. USSR Izv. 20 (1983), 459-492. MR 0661144 (84a:35091)
  • [N] Nirenberg, L., On nonlinear elliptic partial differential equations and Hölder continuity, Comm. Pure Appl. Math. 6 (1953), 103-156. MR 0064986 (16:367c)
  • [S] Safonov, M. V., Unimprovability of estimates of Hölder constants for solutions of linear elliptic equations with measurable coefficients, (Russian) Mat. Sb. (N.S.) 132(174) (1987), no. 2, 275-288; translation in Math. USSR-Sb. 60 (1988), no. 1, 269-281. MR 0882838 (88e:35049)
  • [SY] Sverák, V. and Yan, X., Non-Lipschitz minimizers of smooth uniformly convex functionals, Proc. Natl. Acad. Sci. USA 99 (2002), 15269-15276. MR 1946762 (2003h:49066)
  • [W] Wang, L., On the regularity theory of fully nonlinear parabolic equations I, Comm. Pure Appl. Math. 45 (1992), 27-76. MR 1135923 (92m:35126)

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Additional Information

Nikolai Nadirashvili
Affiliation: LATP, Centre de Mathématiques et Informatique, 39, rue F. Joliot-Curie, 13453 Marseille Cedex, France
Email: nicolas@cmi.univ-mrs.fr

Yu Yuan
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195
Email: yuan@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08367-5
PII: S 0002-9939(06)08367-5
Received by editor(s): November 5, 2004
Posted: January 17, 2006
Additional Notes: Both authors were partially supported by NSF grants, and the second author was also supported by a Sloan Research Fellowship
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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