Variational Formulation of the Dirichlet and Neumann Problems
Let fc G R. We denote by Hk(R2) the standard Sobolev space (see , ,  and ) consisting of three-component distributions u E 5'(IR2) whose Fourier transforms u are regular distributions  generated by functions £&(£), and such that
For a domain S C R2, we denote by Hk(S) the space of the restric tions to S of all the elements of Hk(R2). The norm in H k(S) is defined by
The norm on H k(S) for nonnegative integers k is equivalent to
where a = (oq, a ^ ,<23) 7^ 0 is a multiindex with nonnegative com ponents. From now on we do not distinguish between equivalent norms.