On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems - Davide Guidetti; Sergei Piskarev (Abstract and Applied Analysis)
We give some results concerning the real-interpolation method and finite differences. Next, we apply them to estimate the resolvents of finite-difference discretizations of Dirichlet boundary value problems for elliptic equations in space dimensions one and two in analogs of spaces of continuous and Hölder continuous functions. Such results were employed to study finite-difference discretizations of parabolic equations.