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In Uhlenbecks paper Connections with $L^p$ bounds on curvature [p.38, l. 2-4] it is noted that a certain boundary value problem may be solved by using "boundary value spaces". A book of Katrin Wehrheim uses the same notion, although I was not able to find an explicit definition anywhere. As far as my guess goes, the main idea lies in formulating a boundary value problem as a question on an operator with e.g. range $L^2(\Omega) \times L^2(\partial\Omega)$, where the second factor is the boundary value space.

Question: What is meant by boundary value spaces and what are their advantages when it comes to boundary value problems?

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