A discontinuous Sobolev function exists

Górka, Przemysław; Słabuszewski, Artur

doi:10.1090/proc/14164

A discontinuous Sobolev function exists
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by Przemysław Górka and Artur Słabuszewski PDF

Proc. Amer. Math. Soc. 147 (2019), 637-639 Request permission

Abstract:

We prove that there always exist discontinuous functions in the Hajłasz-Sobolev space $M^{1,s}$ on an $s$-Ahlfors regular metric space when $s>1$. In this way an affirmative answer to the conjecture formulated by X. Zhou (2017) is given.

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