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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 108–118 (Mi ufa172)

On uniform approximability by solutions of elliptic equations of order higher than two

M. Ya. Mazalov

National Research University "Moscow Power Engineering Institute", Smolensk Branch, Smolensk, Russia

Abstract: We consider uniform approximation problems on compact subsets of $\mathbb R^d$, $d>2$, by solutions of homogeneous constant coefficients elliptic equations of order $n>2$. We construct an example showing that in the general case for compact sets with nonempty interior there is no uniform approximability criteria analogous to the well-known Vitushkin's criterion for analytic functions in $\mathbb C$. On the contrary, for nowhere dense compact sets the situation is the same as for analytic and harmonic functions, including instability of the corresponding capacities.

Keywords: elliptic equations, capacities, instability of capacities, uniform approximation, Vitushkin's scheme.

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UDC: 517.5+517.9

Citation: M. Ya. Mazalov, “On uniform approximability by solutions of elliptic equations of order higher than two”, Ufimsk. Mat. Zh., 4:4 (2012), 108–118

Citation in format AMSBIB
\Bibitem{Maz12} \by M.~Ya.~Mazalov \paper On uniform approximability by solutions of elliptic equations of order higher than two \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 4 \pages 108--118 \mathnet{http://mi.mathnet.ru/ufa172}