Remark on the Hӧlder Continuity of p(x)-Harmonic Functions

Аннотация

We consider a p(x)-harmonic equation, where p(x) is measurable in Ω and is separated from 1 and infinity. It is shown that if p(x) is a radial function of x − x₀, in a neighborhood of a point x₀ ∈ Ω i.e., p(x) = p(|x − x₀|) and p(t) is nonincreasing on (0, d), then p(x) is Hӧlder continuous at the point x₀. Bibliography: 11 titles.