On Elliptic Boundary-Value Problems with Small Parameter and Additional Functions on the Boundary of a Domain - Zavorotinskii, A. V. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
We consider elliptic boundary-value problems in which the elliptic operator is a polynomial function of a small parameter and the boundary conditions contain additional unknown functions. It is shown that the condition of ellipticity with small parameter is not only sufficient but also necessary for the a priori estimation of the solutions to this problem in the corresponding special functional spaces depending on the parameter.