Holder quasicontinuity in variable exponent Sobolev spaces

We show that a function in the variable exponent Sobolev spaces coincides with a Holder continuous Sobolev function outside a small exceptional set. This gives us a method to approximate a Sobolev function with Holder continuous functions in the Sobolev norm. Our argument is based on a Whitney-type extension and maximal function estimates. The size of the exceptional set is estimated in terms of Lebesgue measure and a capacity. In these estimates, we use the fractional maximal function as a test function for the capacity. Copyright (C) 2007 Petteri Harjulehto et al.