Elliptic Boundary Value Problem for Dirac-Type Operators: Part 3
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Last time, we studied the hybrid Sobolev spaces using the spectrum of a boundary adapted operator. In particular, the hybrid Sobolev space $\check{H}(A)$ is the image of (extended) trace map on the Dirac-maximal domain, and any boundary condition we will consider is a closed subspace of $\check{H}(A)$. Among all the boundary conditions, a special class called D-elliptic boundary conditions will be the main subject we are discussing. To understand this D-elliptic boundary condition, we will start with the famous APS condition, and try to explore based on that. Under these D-elliptic boundary conditions, nice boundary regularity result is obtained. And we will also discuss many other examples which belong to the class of D-elliptic boundary conditions. References: [Boundary Value Problems for Elliptic Differential Operators of First Order](https://arxiv.org/abs/1101.1196), [Guide to Boundary Value Problems for Dirac-Type Operators](https://arxiv.org/abs/1307.3021)
