Uniqueness Theorems for Goursat-Type Problems

Uniqueness Theorems for 30 Inverse Problems With Incomplete Data

In F&mm, Phys. Lett. 99A, (1983), 258-260, it is proved that a compactly supported inhomogeneity in the velocity profile is uniquely determined by the values of the acoustic pressure collected for aU positions of the source and receiver on the surface of the Earth (on the whole plane P) at low frequencies. Here it is proved that the data collected on Dr x Q2 sufl'ice for the uniqueness theorem ...

Uniqueness Theorems for Inverse Obstacle Scattering Problems in Lipschitz Domains

For the Neumann and Robin boundary conditions the uniqueness theorems for inverse obstacle scattering problems are proved in Lipschitz domains. The role of non-smoothness of the boundary is analyzed.

Uniqueness Theorems for Multidimensional inverse Problems with Unbounded Coefficients

Uniqueness theorems for polyhedra.

In 1813, Cauchy2 gave the first proof of the theorem that two closed convex polyhedra in three-dimensional space are congruent if their faces are congruent in pairs and are joined to each other in the same order: in effect, the a priori possibility of rotations of the faces about the edges-which are obviously seen to be possible for some easily constructed open polyhedra-cannot occur for closed...

Uniqueness Theorems for Cauchy Integrals

If μ is a finite complex measure in the complex plane C we denote by C its Cauchy integral defined in the sense of principal value. The measure μ is called reflectionless if it is continuous (has no atoms) and C = 0 at μ-almost every point. We show that if μ is reflectionless and its Cauchy maximal function Cμ ∗ is summable with respect to |μ| then μ is trivial. An example of a reflectionless m...