The gradient lemma

Volume 91 / 2007

Urban Cegrell Annales Polonici Mathematici 91 (2007), 143-146 MSC: 32U05, 31B05. DOI: 10.4064/ap91-2-4

Abstract

We show that if a decreasing sequence of subharmonic functions converges to a function in $W_{\rm loc}^{1,2}$ then the convergence is in $W_{\rm loc}^{1,2}$.

Authors

  • Urban CegrellUmeå University
    SE-901 87 Umeå, Sweden
    and
    TFM
    Mid Sweden University
    S-851 70 Sundsvall, Sweden
    e-mail

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