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Questions about defining different variable in different equation in subdomain

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Hi,
I am now using PDE model to slove Laplace and Poisson equations. My model has three domains. I have used V as the variable in Laplace equation in two dielectric domains outside and V0 in Poisson equation in the middle water domain. The boundary condition on the interface is V=V0. On the other two sides, the potential are set to be +1V and -1V But the returned value is V0 is always equal to 0 and V is not linear in the dielectric domains. Is this correct?

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