# zbMATH — the first resource for mathematics

On the uniform approximability of functions by polynomial solutions of second-order elliptic equations on compact sets in $$\mathbb R^2$$. (English. Russian original) Zbl 1131.41309
Math. Notes 74, No. 1, 38-48 (2003); translation from Mat. Zametki 74, No. 1, 41-51 (2003).
Summary: The present paper is a continuation of the author’s results [Math. Notes 71, No. 1, 68–79 (2002); translation from Mat. Zametki 71, No. 1, 75–87 (2002; Zbl 1130.41303)]. We study necessary and sufficient conditions for functions to be approximated uniformly on plane compact sets by polynomial solutions to second-order homogeneous elliptic equations with constant coefficients. Sufficient conditions for approximability are of reductive character, i.e., the possibility of approximating on some (simpler) parts of the compact set implies approximability on the entire compact set.

##### MSC:
 41A30 Approximation by other special function classes 35A35 Theoretical approximation in context of PDEs 35J25 Boundary value problems for second-order elliptic equations
Zbl 1130.41303
Full Text: