The mathematical structure of the Poisson equation of Modified Newtonian Dynamics
(MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev
space whose Orlicz function is related to Milgrom’s μ-function, where there exists
existence and uniqueness of weak solutions. Since these do not have in principle
much regularity, a further study is performed where the gravitational field is not
too large, where MOND is most relevant. In that case the field turns out to be
H¨older continuous. Quasilinear MOND is also analyzed.
