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Hölder type quasicontinuity

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Abstract

It is proved that a functionu∈L m,p(R n) (which coincides with the Sobolev spaceW 1,p(R n) ifm=1) coincides with a Hölder continuous functionw outside a set of smallm,q-capacity, whereq<p. Moreover, ifm=1, then the functionw can be chosen to be close tou in theW 1,p-norm.

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  1. Department of Mathematics, Charles University, Sokolovská 83, 18600, Praha 8, Czechia

    Jan Malý

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  1. Jan Malý
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Malý, J. Hölder type quasicontinuity. Potential Anal 2, 249–254 (1993). https://doi.org/10.1007/BF01048508

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  • DOI: https://doi.org/10.1007/BF01048508

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