  The main purpose of this paper is to address some questions concerning
boundary value problems related to the Laplacian and bi-Laplacian operators,
set in the framework of classical $H^s$ Sobolev spaces on a bounded Lipschitz
domain of R^N. These questions are not new and a lot of work has been done in
this direction by many authors using various techniques since the 80's. If for
regular domains almost every thing is elucidated, it is not the case for
Lipschitz ones and for $s$ of the form
  $s = k + 1/2$, with $k$ integer. It is well known that this framework is
delicate. Even in these cases many results are well established but sometimes
not satisfactory. Several questions remain posed. Our main goal through this
work is on one hand to give some improvements to the theory and on another one
by using techniques which do not require too intricate calculations. We also
tried to obtain maximal regularity for the solutions and as far as we can
optimality of the results.
