Regularity for p-harmonic equations with right-hand side in Orlicz–Zygmund classes

We establish regularity results for solutions of some degenerate elliptic PDEs, with right-hand side in a suitable Orlicz–Zygmund class. The nonnegative function which measures the degree of degeneracy of the ellipticity bounds is assumed to be exponentially integrable. We find that the scale of improved regularity is logarithmic and we indicate its exact dependence on the degree of the degeneracy of the problem.