Calculus of Variations and Geometric Measure Theory
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F. Charro - G. De Philippis - A. Di Castro - D. Maximo

On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian

created by dephilipp on 29 Jul 2011
modified on 25 Sep 2012


Accepted Paper

Inserted: 29 jul 2011
Last Updated: 25 sep 2012

Journal: Calc. Var. Partial Differential Equations
Year: 2011


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


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