Continuity at a Point for Solutions to Elliptic Equations with a Nonstandard Growth Condition

A question concerning the Hölder property of solutions to elliptic equations with a nonstandard growth condition is considered. The internal smoothness of solutions to an equation is proved at a fixed point under the condition that a variable exponent at this point has a logarithmic modulus of continuity. The proof is based on a modification of the Moser iteration technique.