|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Sobolev spaces on p.c.f. self-similar sets: boundary behavior and interpolation theorems | | Shiping Cao
; Hua Qiu
; | | Date: |
14 Feb 2020 | | Abstract: | We study the Sobolev spaces $H^sigma(K)$ and $H^sigma_0(K)$ on p.c.f.
self-similar sets in terms of the boundary behavior of functions. First, for
$sigmain mathbb{R}^+$, we make an exact description of the tangents of
functions in $H^sigma(K)$ at the boundary. Second, we characterize
$H_0^sigma(K)$ as the space of functions in $H^sigma(K)$ with zero tangent of
an appropriate order depending on $sigma$. Last, we extend $H^sigma(K)$ to
$sigmainmathbb{R}$, and obtain various interpolation theorems with
$sigmainmathbb{R}^+$ or $sigmainmathbb{R}$. We illustrate that there is a
countable set of critical orders, that arises naturally in the boundary
behavior of functions, such that $H^sigma_0(K)$ presents a critical phenomenon
if $sigma$ is critical. These orders will play a crucial role in our study.
They are just the values in $frac 12+mathbb{Z}_+$ in the classical case, but
are much more complicated in the fractal case. | | Source: | arXiv, 2002.5888 | | 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 claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER