Translator Disclaimer
Autumn 2017 On orthogonal decomposition of a Sobolev space
Dejenie Lakew
Adv. Oper. Theory 2(4): 419-427 (Autumn 2017). DOI: 10.22034/aot.1703-1135

Abstract

The theme of this short article is to investigate an orthogonal decomposition of the Sobolev space $W^{1,2}\left( \Omega \right) $ as $$ W^{1,2}\left( \Omega \right) =A^{2,2}\left( \Omega \right) \oplus D^{2}\left( W_{0}^{3,2}\left( \Omega \right) \right)$$ and look at some of the properties of the inner product therein and the distance defined from the inner product. We also determine the dimension of the orthogonal difference space $W^{1,2}\left( \Omega \right) \ominus \left(W_{0}^{1,2}\left( \Omega \right) \right) ^{\perp }$ and show the expansion of Sobolev spaces as their regularity increases.

Citation

Download Citation

Dejenie Lakew. "On orthogonal decomposition of a Sobolev space." Adv. Oper. Theory 2 (4) 419 - 427, Autumn 2017. https://doi.org/10.22034/aot.1703-1135

Information

Received: 11 March 2017; Accepted: 8 June 2017; Published: Autumn 2017
First available in Project Euclid: 4 December 2017

zbMATH: 1385.46023
MathSciNet: MR3730037
Digital Object Identifier: 10.22034/aot.1703-1135

Subjects:
Primary: 46E35
Secondary: 46C15

Rights: Copyright © 2017 Tusi Mathematical Research Group

JOURNAL ARTICLE
9 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.2 • No. 4 • Autumn 2017
Back to Top