From Heisenberg uniqueness pairs to properties of the Helmholtz and Laplace equations
arXiv:1711.05520
Abstract
The aim of this paper is to establish uniqueness properties of solutions of the Helmholtz and Laplace equations. In particular, we show that if two solutions of such equations on a domain of R d agree on two intersecting d -- 1-dimensional submanifolds in generic position, then they agree everywhere.