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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Uniform approximation by solutions of elliptic equations


Author: Barnet M. Weinstock
Journal: Proc. Amer. Math. Soc. 41 (1973), 513-517
MSC: Primary 35E99; Secondary 35J30, 46J10
DOI: https://doi.org/10.1090/S0002-9939-1973-0340794-0
MathSciNet review: 0340794
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Abstract: The space $ {H_A}(K)$ of continuous functions on a compact set $ K$ in Euclidean space which can be uniformly approximated by solutions of the elliptic, constant-coefficient partial differential equation $ Af = 0$ is studied. In particular, it is shown that $ {H_A}(K)$ is local, in the same sense as in the theory of rational approximation in the complex plane. Simultaneous approximation of functions and their derivatives is also considered.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0340794-0
Keywords: Uniform approximation, elliptic partial differential equations
Article copyright: © Copyright 1973 American Mathematical Society