of an open set
of 
. After introducing a symplectic form on
we obtain
the adjoint of the boundary operator employed.
Full paper in PDF:
Une méthode intégrale de frontière. Application au Laplacien et à l’élasticité
The aim of the paper is to give a method to solve boundary value problems
associated to the Helmholtz equation and to the operator of elasticity. We
transform these problems in problems on the boundary
of an open set
of . After introducing a symplectic form on
we obtain
the adjoint of the boundary operator employed.
Then the boundary problem has a solution if and only if the boundary conditions are orthogonal, for this bilinear form, to the elements of the kernel, in a good space, of the adjoint operator. We illustrate this result for a mixed problem for the Helmholtz equation (th. II.3) and the Dirichlet problem for elasticity (th. III.2), but there exists natural generalizations.
1991 Mathematics Subject Classification: 35J05.