chapter  4
24 Pages

Transmission Boundary Value Problems

We begin with the variational formulation of the transmission (con­ tact) problem (T). We say that u = (u+,u_) G H i jU,(R2) is a weak solution of (T) if

where E +(u,v) and E^{u. v) are the energy density bilinear forms for the plates corresponding to S + and S ~ . We also use the notation

and consider the space R2) equipped with the norm

where q £ R2) is given. Taking v = z £ 2(M2) in (4.1), we conclude that (T) is solvable only if

where u and v are arbitrary representatives of the classes U and V, respectively. It is easy to see that the definitions of B(U, V) and C(V) are consistent.