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Best uniform approximation by solutions of elliptic differential equations

Authors: P. M. Gauthier and D. Zwick
Journal: Trans. Amer. Math. Soc. 342 (1994), 359-374
MSC: Primary 41A50; Secondary 31B99, 35B99
MathSciNet review: 1152322
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Abstract: We investigate best uniform approximations to continuous functions on compact subsets of $ {\mathbb{R}^n}$ by solutions of elliptic differential equations and, in particular, by harmonic functions. An axiomatic setting general enough to encompass problems of this kind is given, and in this context we extend necessary and sufficient conditions for best harmonic approximation on precompact Jordan domains to arbitrary compact sets and to more general classes of solutions of linear elliptic differential equations.

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