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A kinetic equation for a system of elastic hard spheres or disks confined bya hard wall of arbitrary shape is derived. It is a generalization of themodified Enskog equation in which the effects of the confinement are taken intoaccount and it is supposed to be valid up to moderate densities. From theequation, balance equations for the hydrodynamic fields are derived,identifying the collisional transfer contributions to the pressure tensor andheat flux. A Lyapunov functional, $\mathcal{H}[f]$, is identified. For anysolution of the kinetic equation, $\mathcal{H}$ decays monotonically in timeuntil the system reaches the inhomogeneous equilibrium distribution, that is aMaxwellian distribution with a the density field consistent with equilibriumstatistical mechanics.

The Enskog equation for confined elastic hard spheres