3. Given a bounded domain $\Omega \subset \mathbb{R}^d$ with smooth boundary, consider the Robin eigenvalue problem:
$\begin{cases} -\Delta \phi = \lambda \phi, & \text{in } \Omega, \\ n \cdot \nabla \phi = -\kappa \phi, & \text{on } \Gamma, \end{cases}$
where the constant $\kappa > 0$.
(a) Formulate the eigenvalue problem on weak form.
(b) Show that the eigenvalues are positive $\lambda > 0$.
(c) Show that the eigenvalues $\{\lambda_i^N\}_{i=1}^{\infty}$ of the Neumann eigenvalue problem (corresponding to $\kappa = 0$) fulfills $\lambda_i^N \le \lambda_i$ for $i = 1, \dots$
