  A strong comparison principle for semicontinuous viscosity solutions of the
prescribed mean curvature equation is considered. The difficulties of the
problem come from the fact that this nonlinear equation is non-uniformly
elliptic, does not depend on the value of unknown functions, depends on spatial
variables and solutions are semicontinuous. Our simple proof of the strong
comparison principle consists only of three ingredients, the definition of
viscosity solutions, the inf and sup convolutions of functions, and the theory
of classical solutions of quasilinear elliptic equations. Once we have the
strong comparison principle, we can prove a weak comparison principle for
semicontinuous viscosity solutions of the prescribed mean curvature equation in
a bounded domain.
