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A two-dimensional free boundary transmission problem arising in the modelingof an electrostatically actuated plate is considered and a representationformula for the derivative of the associated electrostatic energy with respectto the deflection of the plate is derived. The latter paves the way for theconstruction of energy minimizers and also provides the Euler-Lagrange equationsatisfied by these minimizers. A by-product is the monotonicity of theelectrostatic energy with respect to the deflection.

Stationary states to a free boundary transmission problem for an electrostatically actuated plate