I want to know when the Laplacian is a compact Operator. Do you know some good literature about this topic?
For instance, is the Laplacian compact on the Sobolev space $H^2(\Omega)$? Or maybe on the Hilbert space $C^{\infty}_c(\Omega)$ with the inner product $\langle f,g\rangle:=\int\limits_{\Omega}f\cdot g\text{ }dx$ ?
Thanks you for your answers.