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Quantitative Approximation Theorems for Elliptic Operators

✍ Scribed by Thomas Bagby; Len Bos; Norman Levenberg

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
632 KB
Volume
85
Category
Article
ISSN
0021-9045

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✦ Synopsis

Let L(D) be an elliptic linear partial differential operator with constant coefficients and only highest order terms. For compact sets K/R N whose complements are John domains we prove a quantitative Runge theorem: if a function f satisfies L(D) f=0 on a fixed neighborhood of K, we estimate the sup-norm distance from f to the polynomial solutions of degree at most n. The proof utilizes a two-constants theorem for solutions to elliptic equations. We then deduce versions of Jackson and Bernstein theorems for elliptic operators.

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