The <Alexandrov–Bakelman–Pucci maximum principle> and the absence of a zeroth-order term give
$$
\boxed{|u|_{0;B}\leq C(n,\lambda,\beta)|f|_{0;B}.}
$$
The global <Schauder estimate> is
$$
\boxed{|u|_{2,\alpha;B}
\leq C(n,\alpha,\beta,\lambda)
\big(|f|_{0,\alpha;B}+|u|_{0;B}\big).}
$$
Combining the two bounds gives $|u|_{2,\alpha;B}\leq C|f|_{0,\alpha;B}$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 107 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-107/3/a/solution