Geodesic
A note on global integrability of upper gradients of $p$-superharmonic functions
Outi Elina Maasalo1 ; Anna Zatorska-Goldstein2
1 Institute of Mathematics Helsinki University of Technology P.O. Box 1100 FI-02015 TKK, Finland
2 Institute of Applied Mathematics and Mechanics University of Warsaw Banacha 2 PL-02-097 Warszawa, Poland
Colloquium Mathematicum, Tome 117 (2009) no. 2, pp. 281-288 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider a complete metric space equipped with a doubling measure and a weak Poincaré inequality. We prove that for all $p$-superharmonic functions there exists an upper gradient that is integrable on $H$-chain sets with a positive exponent.
DOI : 10.4064/cm117-2-10
Keywords: consider complete metric space equipped doubling measure weak poincar inequality prove p superharmonic functions there exists upper gradient integrable h chain sets positive exponent

Outi Elina Maasalo 1 ; Anna Zatorska-Goldstein 2

1 Institute of Mathematics Helsinki University of Technology P.O. Box 1100 FI-02015 TKK, Finland
2 Institute of Applied Mathematics and Mechanics University of Warsaw Banacha 2 PL-02-097 Warszawa, Poland 
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Outi Elina Maasalo; Anna Zatorska-Goldstein. A note on global integrability of upper gradients
 of $p$-superharmonic functions. Colloquium Mathematicum, Tome 117 (2009) no. 2, pp. 281-288. doi: 10.4064/cm117-2-10

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