%0 Journal Article
%T H lder Quasicontinuity in Variable Exponent Sobolev Spaces
%A Harjulehto Petteri
%A Kinnunen Juha
%A Tuhkanen Katja
%J Journal of Inequalities and Applications
%D 2007
%I Springer
%X We show that a function in the variable exponent Sobolev spaces coincides with a H lder continuous Sobolev function outside a small exceptional set. This gives us a method to approximate a Sobolev function with H lder 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.
%U http://www.journalofinequalitiesandapplications.com/content/2007/032324