On Elliptic Boundary-Value Problems with Small Parameter and Additional Functions on the Boundary of a Domain
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.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 9, pp 1423-1430.
Citation Example: Zavorotinskii A. V. On Elliptic Boundary-Value Problems with Small Parameter and Additional Functions on the Boundary of a Domain // Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1269–1275.