Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields
Tom 151 / 2002
Studia Mathematica 151 (2002), 31-48
MSC: Primary 35J10, 35B60, 42B20.
DOI: 10.4064/sm151-1-3
Streszczenie
Let $u$ be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset ${\mit \Gamma }$ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for $u^2$ over balls centered at some points near ${\mit \Gamma }$ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.
