From Heisenberg uniqueness pairs to properties of the Helmholtz and Laplace equations. (English) Zbl 1400.35046
Summary: 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 \(\mathbb{R}^d\) agree on two intersecting \(d - 1\)-dimensional submanifolds in generic position, then they agree everywhere.
MSC:
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
Heisenberg uniqueness pair; Helmholtz-Laplace equation; Schwarz reflection principle; harmonic functions; nodal setReferences:
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