We generalize the results in  to higher dimensional ramified spaces. For this purpose we introduce ramified manifolds and, as special cases, locally elementary polygonal ramified spaces (LEP spaces). On LEP spaces we develop a theory of viscosity solutions for Hamilton–Jacobi equations, providing existence and uniqueness results.
Cite this article
Fabio Camilli, Dirk Schieborn, Claudio Marchi, Eikonal equations on ramified spaces. Interfaces Free Bound. 15 (2013), no. 1, pp. 121–140DOI 10.4171/IFB/297