Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces
Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces
We study the convexity preserving property for a class of time-dependent Hamilton-Jacobi equations in a complete geodesic space. Assuming that the Hamiltonian is nondecreasing, we show that in a Busemann space the unique metric viscosity solution preserves the geodesic convexity of the initial value at any time. We provide two …