|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
From Laplacian Transport to Dirichlet-to-Neumann (Gibbs) Semigroups | | Valentin Zagrebnov
; | | Date: |
27 Jan 2008 | | Abstract: | The paper gives a short account of some basic properties of
extit{Dirichlet-to-Neumann} operators $Lambda_{gamma,partialOmega}$
including the corresponding semigroups motivated by the Laplacian transport in
anisotropic media ($gamma
eq I$) and by elliptic systems with dynamical
boundary conditions. For illustration of these notions and the properties we
use the explicitly constructed extit{Lax semigroups}. We demonstrate that for
a general smooth bounded convex domain $Omega subset mathbb{R}^d$ the
corresponding {Dirichlet-to-Neumann} semigroup $left{U(t):= e^{-t
Lambda_{gamma,partialOmega}}
ight}_{tgeq0}$ in the Hilbert space
$L^2(partial Omega)$ belongs to the extit{trace-norm} von Neumann-Schatten
ideal for any $t>0$. This means that it is in fact an extit{immediate Gibbs}
semigroup. Recently Emamirad and Laadnani have constructed a
extit{Trotter-Kato-Chernoff} product-type approximating family
$left{(V_{gamma, partialOmega}(t/n))^n
ight}_{n geq 1}$
extit{strongly} converging to the semigroup $U(t)$ for $n oinfty$. We
conclude the paper by discussion of a conjecture about convergence of the
extit{Emamirad-Laadnani approximantes} in the the { extit{trace-norm}}
topology. | | Source: | arXiv, 0801.4145 | | 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