Skip to content
Part CCSIR NET December 2023eikonal-no-smooth-solution

Eikonal no smooth solution

Let B be the open unit disc in R2,∂B\mathbb{R}^{2}, \partial{}B its boundary and Bˉ=B∪∂B{\bar{B}} = B \cup \partial{}B. For λ∈(0,∞)\lambda \in (0, \infty), let SλS_\lambda be the set of twice continuously differentiable functions in B, continuous on B̄, satisfying (ux)2+λ(uy)2=1(u_{x})^{2} + \lambda(u_y)^{2} = 1 in B and u = 0 on ∂B\partial{}B. Which of the following statements are true?

  1. A.S1=∅S_{1} = \emptyset✓ Correct
  2. B.S2=∅S_{2} = \emptyset✓ Correct
  3. C.S1S_{1} has exactly one element and S2S_{2} has exactly two elements.
  4. D.S1S_{1} and S2S_{2} are both infinite.

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, and why this one tests existence vs uniqueness.

See pricing

50 are analysed free — try those first.

The trap it tests

Existence vs uniqueness

A theorem giving one was read as giving both.

Drill statements like this

Related counterexample: All the classical equations satisfy a maximum principle

More on this topic

The chapter behind this: The three classical equations — free to read

From Partial Differential Equations › Laplace, heat and wave equations: separation of variables

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram