Existence results for the higher order linear Cosserat shell model

Abstract We derive the linear elastic Cosserat shell model of order O ( h 5 ) in the shell thickness h . To this aim, we linearise the geometrically nonlinear elastic Cosserat shell model established previously. Using Korn‐type inequalities for shells, the coercivity of the energy functional and the Lax‐Milgram theorem, we prove the existence and uniqueness of weak solutions to the equilibrium equations.