On improvement of extension operators with the help of approximation operators, with preservation of boundary values (Q1100691)

The author gives a general method of the construction of extension operators on the anisotropic Sobolev spaces. Starting from any extension operator S he establishes an extension operator T which is the best one in the sense of the rate of the growth of highest derivative of the extending function. The method consists in the application to S of the operator of approximation introduced by the first author [Teubner Texte Math. 49, 5-37 (1982; Zbl 0536.46021)] in isotropic and by \textit{E. M. Popova} [Differential equations and functional analysis, Collect. sci. works, Moskva 1985, 76-87 (1985; Zbl 0625.46040)] in anisotropic spaces.