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Title: A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations

Journal Article · · Sbornik. Mathematics
 [1]
  1. Military Academy of Air Defence Forces of Russia Federation named after A. M. Vasilevskii, Smolensk (Russian Federation)

Let X be an arbitrary compact subset of the plane. It is proved that if L is a homogeneous elliptic operator with constant coefficients and locally bounded fundamental solution, then each function f that is continuous on X and satisfies the equation Lf = 0 at all interior points of X can be uniformly approximated on X by solutions of the same equation having singularities outside X. A theorem on uniform piecemeal approximation of a function is also established under weaker constraints than in the standard Vitushkin scheme. Bibliography: 24 titles.

OSTI ID:
21096810
Journal Information:
Sbornik. Mathematics, Vol. 199, Issue 1; Other Information: DOI: 10.1070/SM2008v199n01ABEH003909; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
Country of Publication:
United States
Language:
English