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

Fernando Charro; Guido de Philippis; Agnese Di Castro; Davi Máximo

doi:10.1007/s00526-012-0567-3

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

Fernando Charro, Guido de Philippis, Agnese Di Castro, Davi Máximo

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove L^∞ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-Laplacian, namely, 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.

Original language	English (US)
Pages (from-to)	667-693
Number of pages	27
Journal	Calculus of Variations and Partial Differential Equations
Volume	48
Issue number	3-4
DOIs	https://doi.org/10.1007/s00526-012-0567-3
State	Published - Nov 2013

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-012-0567-3

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abstract = "We prove L∞ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-Laplacian, namely, 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.",

author = "Fernando Charro and {de Philippis}, Guido and {Di Castro}, Agnese and Davi M{\'a}ximo",

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AU - Máximo, Davi

PY - 2013/11

Y1 - 2013/11

N2 - We prove L∞ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-Laplacian, namely, 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.

AB - We prove L∞ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-Laplacian, namely, 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.

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

Abstract

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