The structure of fractional spaces generated by the two-dimensional difference operator on the half plane - Akturk, S.; Ashyralyev, A. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We consider a difference operator approximation A^x_h of the differential operator A^xu(x) = a_11(x)u_x_1 x_1(x) - a_22(x)u_x_2x_2 (x) + σ u(x), x = (x_1, x_2) defined in the region R^+ × R with the boundary condition u(0, x_2) = 0, x_2 R. Here, the coefficients a_ii(x), i = 1, 2, are continuously differentiable, satisfy the uniform ellipticity condition a^2_11(x) + a^2_22(x) ≥ δ > 0. We investigate the structure of the fractional spaces generated by the analyzed difference operator. Theorems on well-posedness in a Holder space of difference elliptic problems are obtained as applications.