Extended Sobolev Scale and Elliptic Operators

• Date: 2013
• Main Authors: Mikhailets, V. A., Murach, A. A., Михайлец, В. А., Мурач, А. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2426
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain a constructive description of all Hilbert function spaces that are interpolation spaces with respect to a couple of Sobolev spaces $[H^{(s_0)}(\mathbb{R}^n), H^{(s_1)}(\mathbb{R}^n)]$ of some integer orders $s_0$ and $s_1$ and that form an extended Sobolev scale. We find equivalent defi...