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A $ C^1$ regularity result for the inhomogeneous normalized infinity Laplacian


Authors: Graziano Crasta and Ilaria Fragalà
Journal: Proc. Amer. Math. Soc. 144 (2016), 2547-2558
MSC (2010): Primary 49K20; Secondary 35J57, 35J70, 49N60
DOI: https://doi.org/10.1090/proc/12916
Published electronically: October 22, 2015
MathSciNet review: 3477071
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Abstract: We prove that the unique solution to the Dirichlet problem with constant source term for the inhomogeneous normalized infinity Laplacian on a convex domain of $ \mathbb{R}^N$ is of class $ C^1$. The result is obtained by showing as an intermediate step the power-concavity (of exponent $ 1/2$) of the solution.


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Graziano Crasta
Affiliation: Dipartimento di Matematica “G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2 – 00185 Roma, Italy
Email: crasta@mat.uniroma1.it

Ilaria Fragalà
Affiliation: Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32 –20133 Milano, Italy
Email: ilaria.fragala@polimi.it

DOI: https://doi.org/10.1090/proc/12916
Received by editor(s): July 9, 2015
Received by editor(s) in revised form: July 17, 2015
Published electronically: October 22, 2015
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society