Affine Approximation of Lipschitz Functions and Nonlinear Quotients

Affine Approximation of Lipschitz Functions and Nonlinear Quotients

New concepts related to approximating a Lipschitz function between Banach spaces by a ne functions are introduced Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X Y for which any Lipschitz function from X to Y can be so approx imated is obtained This is applied to the study of Lipschitz and uniform quotient mapp...

[ m at h . FA ] 1 6 A pr 1 99 8 AFFINE APPROXIMATION OF LIPSCHITZ FUNCTIONS AND NONLINEAR QUOTIENTS

New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X, Y for which any Lipschitz function from X to Y can be so approximated is obtained. This is applied to the study of Lipschitz and uniform quotient ...

Lipschitz quotients from metric trees and from

Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem

Given p e (0, 1), we consider the following problem find u # 0, such that AM = [uf+ =u p in a u = 0 on dO , where Q, er IR is a C 1 domain We prove a near optimal L error bound for the Standard continuous piecewise line ar Galerkin finite element approximation withan acute triangulation In addition we analyse a more practical approximation us ing numerical intégration on the nonlinear term, pro...

Nonlinear Approximation of Random Functions

Given an orthonormal basis and a certain class X of vectors in a Hilbert space H, consider the following nonlinear approximation process: approach a vector x ∈ X by keeping only its N largest coordinates, and let N go to infinity. In this paper, we study the accuracy of this process in the case where H = L(I), and we use either the trigonometric system or a wavelet basis to expand this space. T...