A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations
Journal Article
·
· Sbornik. Mathematics
- 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
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