On Hölder continuity to a function class with nonstandard growth condition.

With the help of De Giorgi's method, the embedding of the $ \mathfrak {B}_{m(x)}(\Omega,M,\gamma,\gamma _1,\delta,\frac {1}{q}) $ B m (x) (Ω , M , γ , γ 1 , δ , 1 q) class into $ C^{0,\alpha }(\Omega) $ C 0 , α (Ω) is proved. This result can be applied to the $ C^{0,\alpha } $ C 0 , α continuity to some elliptic equations with variable exponent. [ABSTRACT FROM AUTHOR]