Inhomogeneous infinity Laplace equation

Advances in Mathematics

Volumn 217, Issue 4, 2008, Pages 1838-1868

  Lu, Guozhen ^a   Wang, Peiyong ^a  

^a WAYNE STATE UNIVERSITY   (United States)

Author keywords

Absolute minimizers; Comparison with standard functions; Infinity Laplace equation; Inhomogeneous equation; Stability of solutions; Viscosity solutions

Indexed keywords

EID: 38348998815     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.11.020     Document Type: Article

References (19)

1. ′ (x)). Ark. Mat. 6 (1965) 33-53
2. ′ (x)). II. Ark. Mat. 6 (1966) 409-431
3. Aronsson G. Extension of functions satisfying Lipschitz conditions. Ark. Mat. 6 (1967) 551-561
4. Aronsson G. Construction of singular solutions to the p-harmonic equation and its limit equation for p = ∞. Manuscripta Math. 56 2 (1986) 135-158
5. Aronsson G., Crandall M., and Juutinen P. A tour of the theory of absolute minimizing functions. Bull. Amer. Math. Soc. 41 4 (2004) 439-505
6. Barles G., and Busca J. Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth-order term. Comm. Partial Differential Equations 26 (2001) 2323-2337
7. ∞ functionals. Arch. Ration. Mech. Anal. 157 4 (2001) 255-283
8. Crandall M.G. An efficient derivation of the Aronsson equation. Arch. Ration. Mech. Anal. 167 4 (2003) 271-279
9. Crandall M.G., and Evans L.C. A remark on infinity harmonic functions. Proceeding of the USA-Chile Workshop on Nonlinear Analysis. Viã del Mar-Valparaiso, 2000. Electron. J. Differ. Equ. Conf. vol. 6 (2001), Southwest Texas State Univ., San Marcos, TX 123-129 (electronic)
10. Crandall M.G., Evans L.C., and Gariepy R.F. Optimal Lipschitz extensions and the infinity Laplacian. Calc. Var. Partial Differential Equations 13 2 (2001) 123-139
11. Crandall M.G., Gunnarsson G., and Wang P. Uniqueness of ∞-harmonic functions and the eikonal equation. Comm. Partial Differential Equations 32 10 (2007) 1587-1615
12. Crandall M.G., Ishii H., and Lions P.L. User's guide to viscosity solutions of second-order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67
13. Crandall M.G., and Wang P. Another Way To Say Caloric. J. Evol. Equ. 3 (2004) 653-672
14. Jensen R. Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient. Arch. Ration. Mech. Anal. 123 1 (1993) 51-74
15. Juutinen P. Minimization problems for Lipschitz functions via viscosity solutions. Ann. Acad. Sci. Fenn. Math. Diss. 115 (1998) 53
16. Lindqvist P., and Manfredi J. The Harnack inequality for ∞-harmonic functions. Electron. J. Differential Equations 4 (1995) approx. 5 pp
17. G. Lu, P. Wang, A PDE perspective of the normalized infinity Laplacian, preprint
18. Manfredi J., Petrosyan A., and Shahgholian H. A free boundary problem for ∞-Laplace equation. Calc. Var. Partial Differential Equations 14 3 (2002) 359-384
19. Peres Y., Schramm O., Sheffield S., and Wilson D. Tug of war and the infinity Laplacian. arXiv: (28 April 2006). math.AP/0605002v1