= Uniqueness of an electrostatic dielectric boundary-value problem
For positive scalar <permittivities> and specified free charges, fixed conductor potentials, <dielectric> matching conditions and decay at infinity, the electrostatic field is unique. Subtract two proposed potentials and integrate $\nabla\cdot(\epsilon\,\delta\phi\nabla\delta\phi)$. The boundary terms vanish or cancel across <dielectric> interfaces, leaving $\int\epsilon|\nabla\delta\phi|^2dV=0$. Hence the difference field is zero, with any potential constant fixed by the boundary convention.
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