Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface
Philippe G. Ciarlet, Oana Iosifescu · Comptes Rendus Mathématique · 2013
In this Note, we establish two Greenʼs formulas with little regularity on a surface. These formulas are then used for identifying and justifying Donati-like compatibility conditions on a surface, guaranteeing that the components of two symmetric matrix fields ( c α β ) and ( r α β ) with c α β and r α β in the space L 2 ( ω ) , where ω is a domain in R 2 , are the covariant components of the linearized change of metric and linearized change of curvature tensors associated with a displacement vector field of a surface θ ( ω ¯ ) , where θ : ω ¯ → R 3 is a smooth immersion.