Remark on the holder continuity of p-harmonic functions

We consider a p(x) -harmonic equation, where p(x) is measurable in [OMEGA] and is separated, from 1 and infinity. It is shown that if p(x) is a radial function of x - [x.sub.0], in a neighborhood of a point [x.sub.0] [member of] [OMEGA] i.e., p(x) = p([absolute value of (x - [x.sub.0])]) and p(t) is nonincreasing on (0, d), then p(x) is Holder continuous at the point [x.sub.0]. Bibliography: 11 titles.