Open Access

Hölder Quasicontinuity in Variable Exponent Sobolev Spaces

Journal of Inequalities and Applications20072007:032324

DOI: 10.1155/2007/32324

Received: 28 May 2006

Accepted: 25 December 2006

Published: 14 February 2007


We show that a function in the variable exponent Sobolev spaces coincides with a Hölder continuous Sobolev function outside a small exceptional set. This gives us a method to approximate a Sobolev function with Hölder 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.


Authors’ Affiliations

Department of Mathematics and Statistics, University of Helsinki
Department of Mathematical Sciences, University of Oulu


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© Petteri Harjulehto et al. 2007

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