On the Resolution of Partial Differential Equations for Lattice Structures on Smooth Manifolds

This paper extends the foundational work presented in "Embedding of a Discrete Lattice Structure in a Smooth Manifold", delving into the mathematical rigor of solving the partial differential equations (PDEs) that underpin the embedding process. It offers analytical solutions to these PDEs, elucidating the geometric interplay between discrete lattices and continuous manifolds within the realm of R^n.