Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 107 / 2 / b

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- Solution b

Solution

The weak maximum principle for elliptic operators fails without a condition at infinity. The function

u (x) = x_{n}

is harmonic on the upper half-space, continuous on its closure, and vanishes on the boundary, but it is positive and unbounded in the interior.

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