On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems.
We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution which is bounded with values in (0 < < 1), with bounded with values in .
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