On the behaviour of ∞ -harmonic functions near isolated points

Nonlinear Analysis, Theory, Methods and Applications

Volumn 58, Issue 3-4, 2004, Pages 333-349

  Bhattacharya, Tilak ^a  

^a BISHOP'S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FUNCTIONS; LAPLACE TRANSFORMS; POISSON EQUATION; THEOREM PROVING;

NEAR ISOLATED POINTS; NONEGATIVE SOLUTIONS; UNBOUNDED SOLUTIONS;

HARMONIC ANALYSIS;

EID: 3042774574     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.02.028     Document Type: Article

References (13)

1. yy=0 Manuscripta Math. 47:1984;133-151.
2. Aronsson G. Construction of singular solutions to the. p -harmonic equation and its limit equation for p→∞ Manuscripta Math. 56:1986;135-158.
3. Barles G., Busca J. Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth order term. Comm. Partial Differential Equations. 26(11-12):2001;2323-2337.
4. Bhattacharya T. An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions. Electron. J. Differential Equations. 44:2001.
5. Bhattacharya T. On the properties of. ∞ -harmonic functions and an application to capacitary convex rings Electron. J. Differential Equation. 2002(101):2002;1-22.
6. p=f and related extremal problems, Rend. Sem. Mat. Univers. Politecn. Torino, Fascicolo Speciale, 1989, Nonlinear PDE's.
7. M.G. Crandall, L.C. Evans, R.F. Gariepy, Optimal Lipschitz extensions and the infinity-Laplacian, Calculus of Variations and Partial Differential Equations, 13 (2) 123-139.
8. Crandall M.G., Ishii H., Lions P.L. User's guide to viscosity solutions of second order partial differential equations. Bull. AMS. 27:1992;1-67.
9. Jensen R. Uniqueness of Lipschitz extensions minimizing the sup-norm of the gradient. Arch. Rational Mech. Anal. 123:1993;51-74.
10. P. Juutinen, P. Lindqvist, J.J. Manfredi, The infinity-Laplacian: examples and observations. Preprint.
11. Kichenassmy L., Laurent V. Singular solutions of the p -Laplace equation Math. Ann. 275(4):1986;599-615.
12. Lindqvist P., Manfredi J.J. The Harnack inequality for. ∞ -harmonic functions Electron. J. Differential Equations. 1995(4):1995;1-5.
13. Manfredi J.J. Isolated singularities of. p -harmonic functions in the plane SIAM J. Math. Anal. 22(2):1991;424-439.