Homogeneous solutions to fully nonlinear elliptic equations
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- by Nikolai Nadirashvili and Yu Yuan
- Proc. Amer. Math. Soc. 134 (2006), 1647-1649
- DOI: https://doi.org/10.1090/S0002-9939-06-08367-5
- Published electronically: January 17, 2006
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Abstract:
We classify homogeneous degree $d\neq 2$ solutions to fully nonlinear elliptic equations.References
- Luis A. Caffarelli and Xavier Cabré, Fully nonlinear elliptic equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, Providence, RI, 1995. MR 1351007, DOI 10.1090/coll/043
- Lawrence C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), no. 3, 333–363. MR 649348, DOI 10.1002/cpa.3160350303
- Qing Han, Nikolai Nadirashvili, and Yu Yuan, Linearity of homogeneous order-one solutions to elliptic equations in dimension three, Comm. Pure Appl. Math. 56 (2003), no. 4, 425–432. MR 1949137, DOI 10.1002/cpa.10064
- Reese Harvey and H. Blaine Lawson Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157. MR 666108, DOI 10.1007/BF02392726
- N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487–523, 670 (Russian). MR 661144
- Louis Nirenberg, On nonlinear elliptic partial differential equations and Hölder continuity, Comm. Pure Appl. Math. 6 (1953), 103–156; addendum, 395. MR 64986, DOI 10.1002/cpa.3160060105
- M. V. Safonov, Unimprovability of estimates of Hölder constants for solutions of linear elliptic equations with measurable coefficients, Mat. Sb. (N.S.) 132(174) (1987), no. 2, 275–288 (Russian); English transl., Math. USSR-Sb. 60 (1988), no. 1, 269–281. MR 882838, DOI 10.1070/SM1988v060n01ABEH003167
- Vladimír Sverák and Xiaodong Yan, Non-Lipschitz minimizers of smooth uniformly convex functionals, Proc. Natl. Acad. Sci. USA 99 (2002), no. 24, 15269–15276. MR 1946762, DOI 10.1073/pnas.222494699
- Lihe Wang, On the regularity theory of fully nonlinear parabolic equations. I, Comm. Pure Appl. Math. 45 (1992), no. 1, 27–76. MR 1135923, DOI 10.1002/cpa.3160450103
Bibliographic 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
- Received by editor(s): November 5, 2004
- Published electronically: 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1647-1649
- MSC (2000): Primary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-06-08367-5
- MathSciNet review: 2204275