A $C^1$ regularity result for the inhomogeneous normalized infinity Laplacian
Copyright policy )A $C^1$ regularity result for the inhomogeneous normalized infinity Laplacian
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.
11 pages. arXiv admin note: text overlap with arXiv:1410.6115
Mathematics - Analysis of PDEs, convex domain, Smoothness and regularity of solutions to PDEs, .Normalized infinity Laplacian; Dirichlet problem; regularity, FOS: Mathematics, Boundary value problems for second-order elliptic systems, Degenerate elliptic equations, 49K20, Dirichlet problem, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, convex domain, Smoothness and regularity of solutions to PDEs, .Normalized infinity Laplacian; Dirichlet problem; regularity, FOS: Mathematics, Boundary value problems for second-order elliptic systems, Degenerate elliptic equations, 49K20, Dirichlet problem, Analysis of PDEs (math.AP)
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