Eikonal equations on ramified spaces
  We generalize the results in [16] 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. 
Fabio Camilli, Dirk Schieborn, Claudio Marchi
math.AP