On the regularity of solutions of the inhomogeneous infinity Laplace equation

Lindgren, Erik

doi:10.1090/S0002-9939-2013-12180-5

On the regularity of solutions of the inhomogeneous infinity Laplace equation
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by Erik Lindgren

Proc. Amer. Math. Soc. 142 (2014), 277-288

DOI: https://doi.org/10.1090/S0002-9939-2013-12180-5

Published electronically: October 2, 2013

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Abstract:

We study the inhomogeneous infinity Laplace equation and prove that for bounded and continuous inhomogeneities, any blow-up is linear but not necessarily unique. If, in addition, the inhomogeneity is assumed to be $C^1$, then we prove that any solution is differentiable, i.e., that any blow-up is unique.

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