POLYGONAL INTERFACE PROBLEMS FOR THE BIHARMONIC OPERATOR

We study some boundary value problems on two-dimensional polygonal top ological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the e dges are inspired by the models introduced by H. Le Dret [13] and Dest uynder and Nevers [9]. The boundary conditions on the external edges a re the classical ones. This class of problem contains the boundary val ue problems for the biharmonic equation in a plane polygon (see [3, 11 , 12, 18]). Conforming to the classical results cited above, we prove that the weak solution of our problem admits a decomposition into a re gular part and a singular part, the latter being a linear combination of singular functions depending on the domain and the considered bound ary value problem. Finally, we give the exact formula for the coeffici ents of these singularities.