Geodesic
Elementary solutions of the Bernstein problem on two intervals
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 1, pp. 63-78 Cet article a éte moissonné depuis la source Math-Net.Ru

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First we note that the best polynomial approximation to $|x|$ on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions. 
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F. Pausinger. Elementary solutions of the Bernstein problem on two intervals. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 1, pp. 63-78. http://geodesic.mathdoc.fr/item/JMAG_2012_8_1_a3/

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