ON A POLYHARMONIC DIRICHLET PROBLEM AND BOUNDARY EFFECTS IN SURFACE SPLINE APPROXIMATION

被引：1

作者：

Hangelbroek, Thomas C. ^{[1
]}

机构：

[1] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 04期

基金：

美国国家科学基金会;

关键词：

surface spline; layer potential; polyharmonic; extension operator; Dirichlet problem; RADIAL-BASIS FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; SCATTERED DATA INTERPOLATION; LIPSCHITZ-DOMAINS; ERROR; ORDER; SPACES; BESOV;

D O I：

10.1137/18M1167188

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For compact domains with smooth boundaries, we present a surface spline approximation scheme that delivers rates in L-p that are optimal for linear approximation in this setting. This scheme can overcome the boundary effects, observed by Johnson [Constr. Approx., 14 (1998), pp. 429-438], by placing centers with greater density near the boundary. It owes its success to an integral identity employing a minimal number of boundary layer potentials, which, in turn, is derived from the boundary layer potential solution to the Dirichlet problem for the m-fold Laplacian. Furthermore, this integral identity is shown to be the "native space extension" of the target function.

引用

页码：4616 / 4654

页数：39

共 50 条

[1] MULTIPLE LAYER POTENTIALS AND THE DIRICHLET PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATIONS IN THE PLANE .1. [J].