The focus of this paper is to show the absence of critical points for the solutions to the Helmholtz equation in a bounded domain Ω⊂ ℝ3, given by (Formula presented.). We prove that for an admissibleg there exists a finite set of frequencies K in a given interval and an open cover Ω¯ = ∪ ω∈KΩω such that |∇uωg(x)|>0 for every ω∈ K and x∈ Ωω. The set K is explicitly constructed. If the spectrum of this problem is simple, which is true for a generic domain Ω , the admissibility condition on g is a generic property.
|Titolo:||Absence of Critical Points of Solutions to the Helmholtz Equation in 3D|
|Data di pubblicazione:||2016|
|Appare nelle tipologie:||01.01 - Articolo su rivista|