Part BCSIR NET December 2024the-exterior-problem-needs-a-condition-at-infinity

The exterior problem needs a condition at infinity

The problem $\partial^{2} u / \partial x^{2} + \partial^{2} u / \partial y^{2} = 0$ in { $(x, y) \in R^{2} : x^{2} + y^{2} > 1$ }, u(x, y) = 1 on { $(x, y) \in R^{2} : x^{2} + y^{2} = 1$ } has

A.no solution
B.exactly one solution
C.exactly two solutions
D.infinitely many solutions✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: All the classical equations satisfy a maximum principle

The exterior problem needs a condition at infinity

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