Communications in Analysis and Geometry

Volume 31 (2023)

Number 1

Boundary unique continuation for the Laplace equation and the biharmonic operator

Pages: 1 – 29

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n1.a1

Author

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

Abstract

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 [$\href{https://doi.org/10.1080/03605309308820929}{\textrm{HK}}$] and [$\href{https://doi.org/10.1080/17476939508814787}{\textrm{HKMP}}$] and by M. S. Baouendi and L. P. Rothschild in [$\href{https://doi.org/10.1155/S1073792893000273}{\textrm{BR1}}$] and [$\href{https://doi.org/10.5802/aif.1375}{\textrm{BR2}}$].

Full Text (PDF format)

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

Received 1 January 2020

Accepted 23 June 2020

Published 21 September 2023