Far field mapping for small sound soft obstacles
Abstract
The extension by continuity of the far field mapping, defined for sound soft obstacles, to the limiting obstacle {0} is studied. We assume that the obstacle is represented in a parametric form: S^{2} nihat xmidrightarrow r(hat x)hat x, where r in C_{+}^{2} (S^{2}). We prove that this extension possesses strong properties of continuity, but cannot be differentiable at {0}, for any reasonably chosen norm. This extends the preceding results of Kirsch (Kirsch A 1993 Inverse Problems 9 8196) and Potthast (Potthast R 1994 Inverse Problems 10 43147).
 Publication:

Inverse Problems
 Pub Date:
 February 2003
 DOI:
 10.1088/02665611/19/1/313
 Bibcode:
 2003InvPr..19..227J