Stability estimates for a class of Helmholtz problems

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.

Keywords

Helmholtz problems, stability estimates, mixed boundary conditions

2010 Mathematics Subject Classification

35B35, 35J05

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Published 1 January 2007