Remarks on Sobolev norms of fractional orders
Analysis of PDEs
2021-01-12 v2
Abstract
When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm as a function on the smaller set compared to its norm on the whole domain? On what do the comparison constants depend on? Do different norms behave differently? This article addresses these issues. We prove some inequalities and disprove some misconceptions by counter-examples.
Keywords
Cite
@article{arxiv.2008.09952,
title = {Remarks on Sobolev norms of fractional orders},
author = {Thanh Tran},
journal= {arXiv preprint arXiv:2008.09952},
year = {2021}
}