Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 447-496 |
| Seitenumfang | 50 |
| Fachzeitschrift | Archive for Rational Mechanics and Analysis |
| Jahrgang | 237 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 10 Apr. 2020 |
| Publikationsstatus | Veröffentlicht - Juli 2020 |
Abstract
For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u, the shape derivative of the Dirichlet energy (with respect to u) is shown to be well-defined and is computed in terms of u. The main difficulties in this context arise from the weak regularity of the domain and the possibly non-empty intersection of the graph of u and the transmission interface. The explicit formula for the shape derivative is then used to identify the partial differential equation solved by the minimizers of an energy functional arising in the modeling of micromechanical systems.
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- Analysis
- Mathematik (insg.)
- Mathematik (sonstige)
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in: Archive for Rational Mechanics and Analysis, Jahrgang 237, Nr. 1, 07.2020, S. 447-496.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Shape Derivative of the Dirichlet Energy for a Transmission Problem
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding Information: Partially supported by the CNRS Projet International de Coopération Scientifique PICS07710.
PY - 2020/7
Y1 - 2020/7
N2 - For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u, the shape derivative of the Dirichlet energy (with respect to u) is shown to be well-defined and is computed in terms of u. The main difficulties in this context arise from the weak regularity of the domain and the possibly non-empty intersection of the graph of u and the transmission interface. The explicit formula for the shape derivative is then used to identify the partial differential equation solved by the minimizers of an energy functional arising in the modeling of micromechanical systems.
AB - For a transmission problem in a truncated two-dimensional cylinder located beneath the graph of a function u, the shape derivative of the Dirichlet energy (with respect to u) is shown to be well-defined and is computed in terms of u. The main difficulties in this context arise from the weak regularity of the domain and the possibly non-empty intersection of the graph of u and the transmission interface. The explicit formula for the shape derivative is then used to identify the partial differential equation solved by the minimizers of an energy functional arising in the modeling of micromechanical systems.
UR - http://www.scopus.com/inward/record.url?scp=85083654098&partnerID=8YFLogxK
U2 - 10.1007/s00205-020-01512-8
DO - 10.1007/s00205-020-01512-8
M3 - Article
AN - SCOPUS:85083654098
VL - 237
SP - 447
EP - 496
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 1
ER -