It is well known that the rate of convergence of the solution u(epsilon) of a singular perturbed problem to the solution u of the unperturbed equation can be measured in terms of the ''smoothness'' of u; smoothness which, in turn, can be expressed in terms of linear interpolation theory. We want to prove a closer relationship between interpolation and singular perturbations, showing that interpolate spaces can be characterized by such a rate of convergence. Furthermore, with respect to a suitable (quite natural) definition of interpolation between convex sets, such a characterization holds true also in the framework of variational inequalities.

Singular perturbation and interpolation

SAVARE', GIUSEPPE
1994-01-01

Abstract

It is well known that the rate of convergence of the solution u(epsilon) of a singular perturbed problem to the solution u of the unperturbed equation can be measured in terms of the ''smoothness'' of u; smoothness which, in turn, can be expressed in terms of linear interpolation theory. We want to prove a closer relationship between interpolation and singular perturbations, showing that interpolate spaces can be characterized by such a rate of convergence. Furthermore, with respect to a suitable (quite natural) definition of interpolation between convex sets, such a characterization holds true also in the framework of variational inequalities.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/116476
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