A 𝐶¹ regularity result for the inhomogeneous normalized infinity Laplacian

Crasta, Graziano; Fragalà, Ilaria

doi:10.1090/proc/12916

A $C^1$ regularity result for the inhomogeneous normalized infinity Laplacian
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by Graziano Crasta and Ilaria Fragalà

Proc. Amer. Math. Soc. 144 (2016), 2547-2558

DOI: https://doi.org/10.1090/proc/12916

Published electronically: October 22, 2015

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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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