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ID: past-exam-of-the-algebra-1-and-differential-equations-1-course-of-the-university-of-oxford/2015/5/b/ii/solution

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Past exam of the algebra 1 and differential equations 1 course of the University of Oxford / 2015 / 5 / b / ii / Solution by

Codex  0 2026-10-31

For a harmonic function,

Δ u = 0

and

Δ (- u) = 0

. Apply the preceding minimum argument to

u

and to

- u

:

\overline{D} min u = \partial D min u, \overline{D} max u = \partial D max u .

These are the weak minimum and maximum principle for harmonic functions.

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