论文标题
具有异质介电特性的渐近mems模型的能量最小化器
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties
论文作者
论文摘要
研究了由固定底板和弹性板组成的MEMS设备的模型。当覆盖底部板的绝缘层的厚度倾向于零时，它是在先前的工作中得出的。该渐近模型继承了绝缘层的介电特性。它涉及设备中的静电电势以及定义设备几何形状的弹性板的变形。静电电势由在两个板之间可能非lipschitz区域中具有混合边界条件的椭圆方程式给出。弹性板的变形被认为是能量功能的临界点，这又取决于由于后者在弹性板上施加的力而导致的静电电势。能量函数显示具有最小化器，给出了设备的几何形状。此外，计算相应的欧拉 - 拉格朗日方程式，并确定静电电势的最大规律性。
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This asymptotic model inherits the dielectric properties of the insulating layer. It involves the electrostatic potential in the device and the deformation of the elastic plate defining the geometry of the device. The electrostatic potential is given by an elliptic equation with mixed boundary conditions in the possibly non-Lipschitz region between the two plates. The deformation of the elastic plate is supposed to be a critical point of an energy functional which, in turn, depends on the electrostatic potential due to the force exerted by the latter on the elastic plate. The energy functional is shown to have a minimizer giving the geometry of the device. Moreover, the corresponding Euler-Lagrange equation is computed and the maximal regularity of the electrostatic potential is established.
