I am thinking about some electrostatic problem. For example, consider a parallel-plate capacitor between x=0 and x=(2a), with a dielectric partially filling it. The dielectric fills the space between x=0 and x-Dd, and y<0. Essentially one quarter of the space inside the capacitor is filled. Of course one could change the size of the region which is filled. The problem is to solve the Laplace equation and find the capacitance.
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