Hölder quasicontinuity in variable exponent sobolev spaces

Petteri Harjulehto*, Juha Kinnunen, Katja Tuhkanen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number032324
Number of pages18
JournalJOURNAL OF INEQUALITIES AND APPLICATIONS
Volume2007
DOIs
Publication statusPublished - 2007
MoE publication typeA1 Journal article-refereed

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