Abstract: In this paper, for the contact without friction for the
Laplacian, theexistence of
necessary and sufficient condition on f
giving a variational solution in is obtained. The proof is based ona priori inequality which is not necessarily true, if W is
a polygon, however, we may prove this a priori inequality with a supplementary
condition This will permit, [6], the calculus
of the index of the problem considered, consequently, if then we can compute the index of
Lamé system using a homotopy of Lamé coefficients.
Keywords and phrases: a priory inequality, Fredholm alternative, Green’s formula, index, Lamé system, Laplacian, oblique derivation, polygon, variational solution.
