Communications in Mathematical Sciences
Volume 5 (2007)
Stability estimates for a class of Helmholtz problems
Pages: 665 – 678
This paper presents new stability estimates for the scalar Helmholtz equation with a complex-valued Robin boundary condition as well as Dirichlet and Neumann boundary conditions. For each estimate, we state the explicit dependency of constants on the wave number. To deal with mixed boundary conditions, we impose geometrical constraints on the two-dimensional or three-dimensional bounded domain.
Helmholtz problems; stability estimates; mixed boundary conditions
2010 Mathematics Subject Classification