2016/11/29 by А. Г. Рамм, Ramm, A. G.
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1611.09598
It is proved that the set of scattering amplitudes \A(β, α, k)\∀ α∈ S2, known for all β∈ S2, where S2 is the unit sphere in ℝ3, k>0 is fixed, k2 is not a Dirichlet eigenvalue of the Laplacian in D, is dense in L2(S2). Here A(β, α, k) is the scattering amplitude corresponding to an obstacle D, where D⊂ ℝ3 is a bounded domain with a boundary S. The boundary condition on S is the Dirichlet condition.