Improved interior regularity for elliptic membrane shells

In this Note we study the regularity of the solution of an obstacle problem for linearly elastic elliptic membrane shells, obtained as a result of a rigorous asymptotic analysis. Since the solution of this boundary value problem is uniquely determined, the problem in object is formulated as a set of variational inequalities posed over a non-empty, closed, and convex subset of a Sobolev space. We will show that, by imposing a higher regularity on the applied body force density acting on the linearly elastic elliptic membrane shell under consideration, the displacement vector field that solves the aforementioned variational inequalities actually enjoys, at least locally, a regularity higher by one order for each of its components