On the Reduction of Coercive Singular Perturbations to Regular Perturbations
Leonid S. Frank, J. J. Heijstek · Birkhäuser Basel eBooks · 1989
It is shown that for a Coercive Singular Perturbation A ɛ appearing in the Linear Elasticity theory, an appropriate choice of a reducing operator S ɛ leads to the asymptotic relation: S ɛ A ɛ = A 0 + ɛ Q ɛ , where A 0 is the reduced operator associated with A ɛ (ɛ = 0) and Q ɛ is a family of continuous linear mappings, uniformly with respect to ɛ ∈ (0, 1], acting from the solution spaces $${{H}^{\varepsilon }}$$ into the data spaces K ɛ .