  We prove an existence result for solutions to the stationary Euler equations
in a domain with nonsmooth boundary. This is an extension of a previous
existence result in smooth domains by Alber (1992). The domains we consider
have a boundary consisting of three parts, one where fluid flows into the
domain, one where the fluid flows out, and one which no fluid passes through.
These three parts meet at right angles. An example of this would be a right
cylinder with fluid flowing in at one end and out at the other, with no fluid
going through the mantle. A large part of the proof is dedicated to studying
the Poisson equation and the related compatibility conditions required for
solvability in this kind of domain.
