Some Biharmonic Problems and their Application in Technology and Medicine

In the present paper we study some properties of solutions of biharmonic problems. Namely, we study the Steklov and Steklov-type boundary value problems for the biharmonic equation. For solving these biharmonic problems with application in technology and medicine, we need to solve the Dirichlet, Neumann and Robin boundary value problems 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, Neumann or Robin, 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.