Biharmonic Problems and their Application in Engineering and Medicine

In the present paper we study some properties of solutions of the Steklov and Neumann boundary value problems for the biharmonic equation. For solving these biharmonic problems with application in engineering and medicine, we need to solve boundary value problems Dirichlet and Cauchy for the Poisson equation using the scattering model. In order to select suitable solutions, we solve the Poisson equation with the corresponding boundary conditions Dirichlet and Cauchy, that is, some criterion function is minimized in the Sobolev norms. Under appropriate smoothness assumptions, these problems may be reformulated as boundary value problems for the biharmonic equation. MSC: 35J15; 35J35; 35J40; 58J50; 58J90.