I'm looking for a good reference for Hodge theory on a compact Riemannian manifold with boundary. I read Section $5.9$ in Taylor's Partial Differential Equations I, which is actually pretty useful in the sense that it has the important theorems (I think), as well as proofs thereof. However, Taylor leaves many gaps for the readers to fill on their own, and I find some of the arguments in this specific section hard to comprehend.
It seems reasonable to believe that there are other texts (either articles or textbooks) which present this theory, but for some reason, I can't find any.
Has anyone of you, dear StackExchange community members, ever bumped into such a text?
Try this book:
Hodge Decomposition -- A Method for Solving Boundary Value Problems by Günter Schwarz.