Inserted: 29 jul 2011
Last Updated: 25 sep 2012
Journal: Calc. Var. Partial Differential Equations
We prove $L^\infty$ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and $p$-Laplacian. We are able to provide a stable family of results depending continuously on the parameter $p$. We also prove the failure of the classical Alexandrov-Bakelman-Pucci estimate for the normalized infinity Laplacian and propose alternate estimates.
Keywords: Infinity Laplacian, A priori estimates, Maximum Principle