Let u be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset Γ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for u² over balls centered at some points near Γ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-3,
author = {Xiangxing Tao},
title = {Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {31-48},
zbl = {0997.35011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-3}
}
Xiangxing Tao. Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields. Studia Mathematica, Tome 151 (2002) pp. 31-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-3/