Equip $C_0^\infty(D)$ with the <Dirichlet inner product>
$$
(f,g)_\nabla=\frac1{2\pi}\int_D\nabla f(x)\mathbin\cdot\nabla g(x)\,dx.
$$
The <zero-boundary Sobolev space> $H_0^1(D)$ is its <Hilbert space completion> in the norm $\|f\|_\nabla=(f,f)_\nabla^{1/2}$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 203 / 4 / a / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-203/4/a/ii/solution