|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Trace operator on von Koch's snowflake | | Krystian Kazaniecki
; Michał Wojciechowski
; | | Date: |
4 Mar 2019 | | Abstract: | We study properties of the boundary trace operator on the Sobolev space
$W^1_1(Omega)$. Using density result by Koskela, Zhang we define a surjective
operator mbox{$Tr: W^1_1(Omega_K)
ightarrow X(Omega_K)$}, where $Omega_K$
is a von Koch snowflake and $X(Omega_K)$ is a trace space with the quotient
norm. Main result of this paper is the existence of a right inverse to $Tr$,
i.e. a linear operator $S: X(Omega_K)
ightarrow W^1_1(Omega_K)$ such that
$Tr circ S= Id_{X(Omega_K)}$. To do this we define an extension of the trace
operator to the space of functions of bounded variation which seems to be new
for domains with fractal boundary. Moreover we identify the isomorphism class
of the trace space. On the other hand, for $Omega$ with regular boundary we
provide a simple proof of the Peetre’s theorem about non-existence of the right
inverse. | | Source: | arXiv, 1903.1100 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER