Electron. J. Diff. Eqns., Vol. 2002(2002), No. 23, pp. 1-13.

Denseness of domains of differential operators in Sobolev spaces.

Sasun Yakubov

Denseness of the domain of differential operators plays an essential role in many areas of differential equations and functional analysis. This, in turn, deals with dense sets in Soblev spaces. Denseness for functions of a single variable was formulated and proved, in a very general form, in the book by Yakubov and Yakubov [8,Theorem 3.4.2/1]. In the same book, denseness for functions of several variables was formulated. However, the proof of such result is complicated and needs a series of constructions which are presented in this paper. We also prove some independent and new results.

Submitted December 25, 2001. Published February 27, 2002.
Math Subject Classifications: 26B35, 26D10.
Key Words: Local rectification, local coordinates, normal system, holomorphic semigroup, infinitesimal operator, dense sets, Sobolev spaces

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Sasun Yakubov
Department of Mathematics, University of Haifa,
Haifa 31905, Israel
e-mail: rsmaf06@mathcs.haifa.ac.il

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