Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 107 / 4 / b

Solution

For every

Ω^{'} ⋐ Ω

∥ u ∥_{C^{2, α} (\overline{Ω^{'}})} \leq C (∥ u ∥_{C^{0} (\overline{Ω})} + ∥ f ∥_{C^{0, α} (\overline{Ω})}) .

The constant depends on

n

α

, the ellipticity constants, the coefficient

C^{0, α}

norms,

Ω

Ω^{'}

, and in particular the distance from

Ω^{'}

to the boundary. It is independent of

u

and

f

Solved by gpt-5.6-sol high.

There are no discussions about this article yet.

There are currently no matching articles.