Geodesic
An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We present an elementary proof of the Harnack inequality for non-negative viscosity supersolutions of $\Delta_{\infty}u=0$. This was originally proven by Lindqvist and Manfredi using sequences of solutions of the p-Laplacian. We work directly with the $\Delta_{\infty}$ operator using the distance function as a test function. We also provide simple proofs of the Liouville property, Hopf boundary point lemma and Lipschitz continuity.
Classification : 35J70, 26A16
Keywords: viscosity solutions, Harnack inequality, infinite harmonic operator, distance function 
@article{EJDE_2001__2001__a104,
     author = {Bhattacharya, Tilak},
     title = {An elementary proof of the {Harnack} inequality for non-negative infinity-superharmonic functions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a104/}
}
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Bhattacharya, Tilak. An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a104/