A Boundary Differential Equation for Thin Shells

We present a mathematical construction of boundary equations for thin shells from classical elasticity by using the differential boundary calculus and the oriented distance function. This model extends to thin shells the "natural theory" and the theory of Love-Kirchhoff as given by Germain for plates. We specify the appropriate function spaces and give existence and uniqueness theorems. We conjecture that our second order model is related to the one of Naghdi, and that the fourth order model is related to the one of Koiter.