Various properties of solutions of the infinity-Laplacian equation

Communications in Partial Differential Equations

Volumn 30, Issue 7-9, 2005, Pages 1401-1428

  Evans, Lawrence C ^a   Yu, Yifeng ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Degenerate elliptic equations; Infinity Laplacian; Viscosity solutions

Indexed keywords

EID: 27744464019     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300500258956     Document Type: Article

References (13)

1. Aronsson, G. (1967). Extension of functions satisfying Lipschitz conditions. Arkiv für Mate. 6:551-561.
2. yy = 0. Arkiv für Mate. 7:395-425.
3. yy = 0. Manuscripta Math. 47:133-151.
4. ∞. In: Clarke, Stern, ed. Nonlinear Analysis, Differential Equations and Control. Kluwer Academic.
5. Bhattacharya, T. (2005). On the behavior of ∞-harmoninc functions near isolated points. Nonlinear Analysis 58:333-349.
6. Crandall, M. G., Evans, L. C. (2001). A remark on infinity harmonic functions. Electronic Journal of Differential Equations Conf 06:123-129.
7. Crandall, M. G., Evans, L. C., Gariepy, R. F. (2001). Optimal Lipschitz extensions and the infinity Laplacian. Calculus of Variations and Partial Differential Equations 13:123-139.
8. Evans, L. C. (2003a). Some new PDE methods for weak KAM theory. Calculus of Variations and Partial Differential Equations 17:159-177.
9. Evans, L. C. (2003b). Three singular variational problems. Viscosity Solutions of Differential Equations and Related Topics. RIMS Kokyuroku 1323. Research Institute for the Matematical Sciences.
10. Fathi, A. (2004). The Weak KAM Theorem in Lagrangian Dynamcis. Cambridge Studies in Advanced Mathematics. New York: Cambridge University Press.
11. Jensen, R. (1993). Uniqueness of Lipschitz extensions minimizing the sup-norm of the gradient. Arch. Rat. Mech. Analysis 123:51-74.
12. Oberman, A. (2005). Convergent difference scheme approximations for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions. Math. Comp. 74:1217-1230.
13. 1 regularity for infinity harmonic fuctions in two dimensions. Arch. Rational Mech. Analysis 176:351-361.