@article {
author = {Lakew, Dejenie},
title = {On orthogonal decomposition of a Sobolev space},
journal = {Advances in Operator Theory},
volume = {2},
number = {4},
pages = {419-427},
year = {2017},
publisher = {Tusi Mathematical Research Group (TMRG)},
issn = {2538-225X},
eissn = {2538-225X},
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.},
keywords = {Sobolev space,orthogonal decomposition,,inner product,Distance},
url = {http://www.aot-math.org/article_46656.html},
eprint = {http://www.aot-math.org/article_46656_2f36d0c24bbc89d4e269167986e59a54.pdf}
}