Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1679-1688 |
| Seitenumfang | 10 |
| Fachzeitschrift | Zeitschrift fur Angewandte Mathematik und Physik |
| Jahrgang | 64 |
| Publikationsstatus | Veröffentlicht - 28 Feb. 2013 |
| Extern publiziert | Ja |
Abstract
Let Ω ⊂ ℝN be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ∂Ω. We show that the solution to the linear first-order system (Formula is Presented) is unique if (Formula is Presented) and (Formula is Presented). As a consequence, we prove (Formula is Presented) to be a norm for (Formula is Presented) for some p, q > 1 with 1/p + 1/q = 1 as well as det (Formula is Presented). We also give a new and different proof for the so-called 'infinitesimal rigid displacement lemma' in curvilinear coordinates: Let (Formula is Presented) satisfy sym (Formula is Presented) for some (Formula is Presented). Then, there exist a constant translation vector (Formula is Presented).
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Mathematik (insg.)
- Angewandte Mathematik
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in: Zeitschrift fur Angewandte Mathematik und Physik, Jahrgang 64, 28.02.2013, S. 1679-1688.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Uniqueness of integrable solutions to ∇ ζ=G ζ, ζǀGamma = 0 for integrable tensor coefficients G and applications to elasticity
AU - Lankeit, Johannes
AU - Neff, Patrizio
AU - Pauly, Dirk
PY - 2013/2/28
Y1 - 2013/2/28
N2 - Let Ω ⊂ ℝN be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ∂Ω. We show that the solution to the linear first-order system (Formula is Presented) is unique if (Formula is Presented) and (Formula is Presented). As a consequence, we prove (Formula is Presented) to be a norm for (Formula is Presented) for some p, q > 1 with 1/p + 1/q = 1 as well as det (Formula is Presented). We also give a new and different proof for the so-called 'infinitesimal rigid displacement lemma' in curvilinear coordinates: Let (Formula is Presented) satisfy sym (Formula is Presented) for some (Formula is Presented). Then, there exist a constant translation vector (Formula is Presented).
AB - Let Ω ⊂ ℝN be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ∂Ω. We show that the solution to the linear first-order system (Formula is Presented) is unique if (Formula is Presented) and (Formula is Presented). As a consequence, we prove (Formula is Presented) to be a norm for (Formula is Presented) for some p, q > 1 with 1/p + 1/q = 1 as well as det (Formula is Presented). We also give a new and different proof for the so-called 'infinitesimal rigid displacement lemma' in curvilinear coordinates: Let (Formula is Presented) satisfy sym (Formula is Presented) for some (Formula is Presented). Then, there exist a constant translation vector (Formula is Presented).
KW - First-order system of partial differential equations
KW - Generalized Korn's first inequality
KW - Infinitesimal rigid displacement lemma
KW - Korn's inequality
KW - Korn's inequality in curvilinear coordinates
KW - Unique continuation
KW - Uniqueness
UR - http://www.scopus.com/inward/record.url?scp=84892899765&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1209.3388
DO - 10.48550/arXiv.1209.3388
M3 - Article
AN - SCOPUS:84892899765
VL - 64
SP - 1679
EP - 1688
JO - Zeitschrift fur Angewandte Mathematik und Physik
JF - Zeitschrift fur Angewandte Mathematik und Physik
SN - 0044-2275
ER -