Résumé
Let Ω be an open subset of R n and f:Ω→R a continuous function. A superharmonic majorant of f in Ω is called minimal if it is harmonic in the (open) set where if differs from f. Many properties of these functions are similar to those of nonnegative harmonic functions in Ω (in fact the case f=0); e.g. the whole family is uniformly equicontinuous in each compact subset of Ω, with respect to the uniform structure of R ‾. Application is made to the “Dirichlet” problem of finding a minimal superharmonic majorant of f agreeing with given boundary values (a problem arising from the mechanics of continua and formerly studied by hilbertian methods).