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math.AP2026
Stability and Perron's method for Monge solutions of eikonal equations in metric spaces
Qing Liu, Made Benny Prasetya Wiranata
The main result of this paper concerns the stability of Monge solutions to eikonal equations in metric spaces. Although the subslope used in the standard definition of Monge soluti…
math.AP2025
Superposition Property in Disjoint Variables for the Infinity Laplace Equation
Qing Liu, Juan J. Manfredi, Xiaodan Zhou
We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infin…
math.AP2025
Monge solutions of time-dependent Hamilton-Jacobi equations in metric spaces
Qing Liu, Made Benny Prasetya Wiranata
As a classical notion equivalent to viscosity solutions, Monge solutions are well understood for stationary Hamilton-Jacobi equations in Euclidean spaces and have been recently stu…