Local boundary value problems for Dirac type operators (Q610298)

This paper is concerned with the study of Euclidean Dirac type operators. The first part of this paper goes back as far as the classical problem of determining a holomorphic function in a plane domain from its real part. More precisely, to each Dirac type operator there is assigned a formally exact elliptic complex of length 2. The authors study the Neumann problem and they derive a weak orthogonal decomposition. In the final part of the paper, it is shown how the Dirichlet norm can be used to establish the solvability of the Neumann problem. The most difficult step in the study of the Neumann problem consists in proving the regularity of the Neumann operator. A crucial part in the proof of the solvability is the Kohn-Nirenberg estimate.