# Eigenvalue/function of Laplace Operator for Exterior of Disk - Reference Request

I'd like to know more about,

$$\lambda u = \nabla ^2 u$$

for unbounded domains (particularly the exterior of a disk in $$\mathbb{R}^2$$ or ball in $$\mathbb{R}^3$$), but have had a hard time finding references online. Can anyone suggest a website or book that covers this in depth? i.e. How to obtain solutions, proofs, important corollaries/theorems, etc.

• Have you tried separation of variablaes? – DisintegratingByParts Oct 2 '18 at 22:02
• Facepalm... will try that first.... although, the reason I bring it up is because I recall that unbounded domains can dramatically alter the nature of the eigenvalues. But first things first. – Eric Oct 2 '18 at 22:25
• It's natural to restrict to $L^2$ solutions on the exterior domain. – DisintegratingByParts Oct 4 '18 at 2:36