Communications in Analysis and Geometry

Volume 31 (2023)

Number 1

Boundary unique continuation for the Laplace equation and the biharmonic operator

Pages: 1 – 29



S. Berhanu (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)


We establish results on unique continuation at the boundary for the solutions of $\Delta u = f$, $f$ harmonic, and the biharmonic equation $\Delta^2 u = 0$. The work is motivated by analogous results proved for harmonic functions by X. Huang et al in [$\href{}{\textrm{HK}}$] and [$\href{}{\textrm{HKMP}}$] and by M. S. Baouendi and L. P. Rothschild in [$\href{}{\textrm{BR1}}$] and [$\href{}{\textrm{BR2}}$].

The author’s work was supported in part by NSF DMS 1855737.

Received 1 January 2020

Accepted 23 June 2020

Published 21 September 2023