Details
| Original language | English |
|---|---|
| Article number | 2 |
| Journal | Nonlinear Differential Equations and Applications |
| Volume | 30 |
| Issue number | 1 |
| Early online date | 20 Oct 2022 |
| Publication status | Published - Jan 2023 |
Abstract
A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the deflection of the plate is derived. The latter paves the way for the construction of energy minimizers and also provides the Euler–Lagrange equation satisfied by these minimizers. A by-product is the monotonicity of the electrostatic energy with respect to the deflection.
Keywords
- Minimizers, Obstacle problem, Shape derivative, Transmission problem
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Nonlinear Differential Equations and Applications, Vol. 30, No. 1, 2, 01.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stationary states to a free boundary transmission problem for an electrostatically actuated plate
AU - Laurençot, Philippe
AU - Walker, Christoph
N1 - Funding Information: Part of this work was done while PhL enjoyed the hospitality and support of the Institut für Angewandte Mathematik, Leibniz Universität Hannover. We express our gratitude to the anonymous referees for their helpful comments.
PY - 2023/1
Y1 - 2023/1
N2 - A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the deflection of the plate is derived. The latter paves the way for the construction of energy minimizers and also provides the Euler–Lagrange equation satisfied by these minimizers. A by-product is the monotonicity of the electrostatic energy with respect to the deflection.
AB - A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the deflection of the plate is derived. The latter paves the way for the construction of energy minimizers and also provides the Euler–Lagrange equation satisfied by these minimizers. A by-product is the monotonicity of the electrostatic energy with respect to the deflection.
KW - Minimizers
KW - Obstacle problem
KW - Shape derivative
KW - Transmission problem
UR - http://www.scopus.com/inward/record.url?scp=85140220199&partnerID=8YFLogxK
U2 - 10.1007/s00030-022-00809-9
DO - 10.1007/s00030-022-00809-9
M3 - Article
AN - SCOPUS:85140220199
VL - 30
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
SN - 1021-9722
IS - 1
M1 - 2
ER -