On the uniqueness of the solution for the boundary value problem of infinite order (Q807881)

This paper consists of three sections. In section one and in section two the authors study principal properties and criteria of nontriviality for Sobolev-Orlicz spaces of infinite order. In section three, they prove that under suitable conditions the Dirichlet problem for the elliptic equations of infinite order \[ \sum^{\infty}_{| \alpha | =0}(-1)^{| \alpha |}D^{\alpha}(x,u,Du,...,D^{\alpha}u)=h(x),\quad x\in \Omega;\quad D^ wu|_{\partial \Omega}=0,\quad | w| =0,1,... \] possesses a unique solution.