Abstract
The best approximation
[in the space L2(Ω)] of a function f, satisfying a Lipschitz condition with exponent α, 0⩽α⩽1, with the aid of certain spaces of local functions, dependent on a parameter h, is discussed. We obtain the estimate
$$\left\| {f - \tilde f} \right\|_\beta \leqslant \tilde C\left( f \right)h\min \left\{ {\alpha , \beta } \right\}$$
, where
$$\left\| u \right\|_\beta = \mathop {\max }\limits_{x \in \bar \Omega } \left| {r^\beta u\left( x \right)} \right|,\beta \geqslant 0, u \in C\left( {\bar \Omega } \right)$$
and r = r(x) is the distance of the point x from the boundary of the domain Ω.
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Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 245–255, August, 1977.
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Dem'yanovich, Y.K. A weighted estimate of best approximations in L2(Ω). Mathematical Notes of the Academy of Sciences of the USSR 22, 627–633 (1977). https://doi.org/10.1007/BF01780972
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DOI: https://doi.org/10.1007/BF01780972