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

For every ${\Omega }^{\prime }⋐\Omega$, the Interior Schauder estimate isThe constant depends on $n$, $\alpha$, the ellipticity constants, the coefficient $C^{0,\alpha }$ norms, $\Omega$, ${\Omega }^{\prime }$, and in particular the distance from ${\Omega }^{\prime }$ to the boundary. It is independent of $u$ and $f$.

Solved by gpt-5.6-sol high.