Partial regularity of solutions of fully nonlinear, Uniformly elliptic equations

Communications on Pure and Applied Mathematics

Volumn 65, Issue 8, 2012, Pages 1169-1184

  Armstrong, Scott N ^a   Silvestre, Luis E ^a   Smart, Charles K ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84861455886     PISSN: 00103640     EISSN: 10970312     Source Type: Journal    
DOI: 10.1002/cpa.21394     Document Type: Article

References (11)

1. 2, α regularity theory for a class of non-convex fully nonlinear elliptic equations. J. Math. Pures Appl. (9) 82 (2003), no. 5, 573-612.
2. Caffarelli, L. A.; Cabré, X. Fully nonlinear elliptic equations. American Mathematical Society Colloquium Publications, 43. American Mathematical Society, Providence, R.I., 1995.
3. Caffarelli, L. A.; Silvestre, L. On the Evans-Krylov theorem. Proc. Amer. Math. Soc. 138 (2010), no. 1, 263-265.
4. Caffarelli, L. A.; Souganidis, P. E. A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Comm. Pure Appl. Math. 61 (2008), no. 1, 1-17.
5. Evans, L. C. Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math. 35 (1982), no. 3, 333-363.
6. Krylov, N. V. Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), no. 1, 75-108; English translation: Math. USSR Izv. 22 (1984), no. 1, 67-98.
7. p-estimates for elliptic equations of nondivergent type. Proc. Amer. Math. Soc. 96 (1986), no. 3, 447-451.
8. Nadirashvili, N.; Vlǎduţ, S. Nonclassical solutions of fully nonlinear elliptic equations. Geom. Funct. Anal. 17 (2007), no. 4, 1283-1296.
9. Nadirashvili, N.; Vlǎduţ, S. Singular viscosity solutions to fully nonlinear elliptic equations. J. Math. Pures Appl. (9) 89 (2008), no. 2, 107-113.
10. Savin, O. Small perturbation solutions for elliptic equations. Comm. Partial Differential Equations 32 (2007), no. 4-6, 557-578.
11. Yuan, Y. A priori estimates for solutions of fully nonlinear special Lagrangian equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), no. 2, 261-270.