Uniqueness theorems for certain improperly posed problems

A Mollification Framework for Improperly Posed Problems

1. Introduction Various authors have explored the role of molliication in the solution of improperly posed problems such as numerical diierentiation and the numerical solution of rst kind integral equations. For example, Murio 13], exploiting earlier suggestions of Manselli and Miller 11] as well as Vasin 16], has shown how molliied numerical diierentiators can be constructed for the diierentia...

The Finite Element Method in a Family of Improperly Posed Problems

The numerical solution of the Cauchy problem for elliptic equations is considered. We reformulate the original problem as a variational inequality problem, which we solve using the finite element method. Moreover, we prove the convergence of the approximate solution. Let <$> be a bounded open set in the space R" and d6^ be the boundary of fy. Then ßr = ty X (0, T) is a bounded open set in Rn+I....

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