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.
A C^1 regularity result for the inhomogeneous normalized infinity Laplacian / Crasta, Graziano; Fragalà, Ilaria. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 144:(2016), pp. 2547-2558. [10.1090/proc/12916]
A C^1 regularity result for the inhomogeneous normalized infinity Laplacian
CRASTA, Graziano;
2016
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.File allegati a questo prodotto
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