Eikonal equations on ramified spaces

Eikonal equations on ramified spaces

Generalization of the viscosity solution theory for Hamilton–Jacobi equations to higher-dimensional ramified spaces (LEP-Spaces). With Fabio Camilli and Claudio Marchi, 2013.

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Authors: Fabio Camilli, Dirk Schieborn, Claudio Marchi

Journal: Interfaces and Free Boundaries

Reference: DOI 10.4171/IFB/297

Year of publication: 2013

Abstract

We generalize the results of [23] to higher-dimensional ramified spaces. To this end, we introduce ramified manifolds and — as a special case — locally elementary polygonal ramified spaces (LEP-Spaces). On LEP-Spaces we develop a theory of viscosity solutions for Hamilton–Jacobi equations and provide existence and uniqueness results.