## 2.3 Direct BEM for the plate equation

### 2.3.1 Rayleigh-Green identity

Consider the two-dimensional multiply connected domain $\mathrm{\Omega}$ of the $\mathit{xy}$ plane occupied by the plate. The domain is bounded by the $\mathit{K}+1$ non-intersecting curves ${\mathrm{\Gamma}}_{0},{\mathrm{\Gamma}}_{1},\dots ,{\mathrm{\Gamma}}_{\mathit{K}}$, forming the boundary $\mathrm{\Gamma}={\displaystyle {\cup}_{\mathit{k}=0}^{\mathit{K}}{\mathrm{\Gamma}}_{\mathit{k}}}$ of the plate, which may be piecewise smooth, i.e., it may have a finite number of corners ...

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