  We consider the incompressible Euler equations in a bounded domain in three
space dimensions. Recently, the first two authors proved Onsager's conjecture
for bounded domains, i.e., that the energy of a solution to these equations is
conserved provided the solution is H\"older continuous with exponent greater
than 1/3, uniformly up to the boundary. In this contribution we relax this
assumption, requiring only interior H\"older regularity and continuity of the
normal component of the energy flux near the boundary. The significance of this
improvement is given by the fact that our new condition is consistent with the
possible formation of a Prandtl-type boundary layer in the vanishing viscosity
limit.
