Abstract
We study a linear elliptic partial differential equation of second order in a bounded domain ? ? R N , with nonstandard boundary conditions on a part ? of the boundary ??. Here, neither the solution nor its normal derivative are prescribed pointwise. Instead, the average of the solution over ? is given and the normal derivative along ? has to follow a prescribed shape function, apart from an additive (unknown) constant. We prove the well-posedness of the problem and provide a method for the recovery of the unknown boundary data.
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