Creating desired potentials by embedding small inhomogeneities

Details Creating desired potentials by embedding small inhomogeneities Creating desired potentials by embedding small inhomogeneities

2009-06-17

arxiv.org/abs/0906.3214v1

Physics

Mathematical Physics

Scientific paper

The governing equation is $[\nabla^2+k^2-q(x)]u=0$ in $\R^3$. It is shown that any desired potential $q(x)$, vanishing outside a bounded domain $D$, can be obtained if one embeds into D many small scatterers $q_m(x)$, vanishing outside balls $B_m:=\{x: |x-x_m|

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