Abstract
We prove some regularity results for the solution of a linear abstract Cauchy problem of parabolic type. As an application, we study the approximation of the solution by means of an implicit-Euler discretization in time, which is stable with respect to a wide class of Galerkin approximation methods in space. The error is evaluated in norms of typeL 2(0, ?,L 2) andL 2(0, ?,V)?(H 00 1/2 (0, ?,H)+H 1(0, ?,V?)), whereV?H?V? are Hilbert spaces (the embeddings are supposed to be dense and continuous). We prove error estimates which are optimal with respect to the regularity assumptions on the right-hand side of the equation.
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