Well-posedness of the difference schemes for elliptic equations in \(C_\tau^{\beta,\gamma}(E)\) spaces (Q1003882)

The paper deals with a second order of accuracy difference scheme for the periodic (nonlocal) boundary value problem \[ -v''(t)+Av(t)=f(t), \; t \in (0,1), \] \[ v(0)=v(1), \; v^{\prime}(0)=v^{\prime}(1) \] with a strongly positive operator coefficient \(A\) in a Banach space. A series of coercivity inequalities in difference analogues of various Hölder norms is obtained and the well-posedness of the difference scheme in \(C_{\tau}^{\beta, \gamma}(E)\) spaces is proved. An example of an elliptic \(2m\)-order multidimensional partial differential equation is considered.