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We develop an elliptic theory based in $L^2$ of boundary value problems forgeneral wedge differential operators of first order under only mild assumptionson the boundary spectrum. In particular, we do not require the indicial rootsto be constant along the base of the boundary fibration.  Our theory includes as a special case the classical theory of ellipticboundary value problems for first order operators with and without theShapiro-Lopatinskii condition, and can be thought of as a natural extension ofthat theory to the geometrically and analytically relevant class of wedgeoperators. Wedge operators arise in the global analysis on manifolds withincomplete edge singularities. Our theory settles, in the first order case, thelong-standing open problem to develop a robust elliptic theory of boundaryvalue problems for such operators.

Boundary value problems for first order elliptic wedge operators