Interpolation in a ball with a minimum value of the L p-Norm of the Laplace operator

Abstract

We consider the problem of interpolation of finite sets of numerical data bounded in L p-norms (1 ≤ p < ∞) by smooth functions that are defined in an n-dimensional Euclidean ball of radius R and vanish on the boundary of the ball. Under some constraints on the location of interpolation nodes, we obtain two-sided estimates with a correct dependence on R for the L p-norms of the Laplace operators of the best interpolants. © 2012 Pleiades Publishing, Ltd.