Uniqueness theorem for Poisson's equation: Difference between revisions

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# Modified [[Neumann boundary condition]] (also called [[Robin boundary condition]] - conditions where boundaries are specified as conductors with known charges): <math>\mathbf{\nabla}\varphi</math> is also well defined by applying locally [[Gauss's Law]]. As such, the surface integral also vanishes.

# Mixed boundary conditions (a combination of Dirichlet, Neumann, and modified Neumann boundary conditions): the uniqueness theorem will still hold.

The boundary surfaces may also include boundaries at infinity (describing unbounded domains) - for these as well the uniqueness theorem holds if the surface integral vanishes, which is the case (for example) when at large distances the integrand decays faster than the surface area grows.

==See also==