The gradient lemma
Volume 91 / 2007
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 $W_{\rm loc}^{1,2}$.
