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Comparison principle to the infinity Laplacian equation with lower term

Volume 6, Issue 5, October 2021    |    PP. 51-62    |PDF (395 K)|    Pub. Date: November 9, 2021
DOI: 10.54647/mathematics11292    10 Downloads     530 Views  

Author(s)
Cuicui Li, School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People’s Republic of China
Fang Liu, School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People’s Republic of China

Abstract
In this paper, we establish the comparison principles via the perturbation method for the equation in , where is a highly degenerate and h- homogeneous operator associated with the infinity Laplacian. Based on the comparison principle, we obtain the uniqueness of the viscosity solution to the Dirichlet problem

where During this procedure, we also establish a stability result of the viscosity solution to the inhomogeneous equation.

Keywords
infinity Laplacian; viscosity solutions; comparison principle; stability.

Cite this paper
Cuicui Li, Fang Liu, Comparison principle to the infinity Laplacian equation with lower term, SCIREA Journal of Mathematics. Vol. 6 , No. 5 , 2021 , pp. 51 - 62 . https://doi.org/10.54647/mathematics11292

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