  About thirty years ago we looked for "minimal assumptions" on the data which
guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a
bounded domain are classical. Classical means here that all the derivatives
appearing in the equations and boundary conditions are continuous up to the
boundary. Following a well known device, the above problem led us to consider
this same regularity problem for the Poisson equation under homogeneous
Dirichlet boundary conditions. At this point, one was naturally led to consider
the extension of this last problem to more general linear elliptic boundary
value problems, and also to try to extend the results to more general data
spaces. At that time, some side results in these directions remained
unpublished. The first motivation for this note is a clear description of the
route followed by us in studying these kind of problems. New results and open
problems are also considered.
