In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show thatâ€¦ (More)

In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as theâ€¦ (More)

We construct complex geometrical optics solutions for the isotropic elasticity system concentrated near spheres. We then use these special solutions, called complex spherical waves, to identifyâ€¦ (More)

We develop a reconstruction algorithm to determine penetrable obstacles inside a domain in the plane from acoustic measurements made on the boundary. This algorithm uses complex geometrical opticsâ€¦ (More)

We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokesâ€¦ (More)

We consider the reconstruction of elastic inclusions embedded inside of a planar region, bounded or unbounded, with isotropic inhomogeneous elastic parameters by measuring displacements and tractionsâ€¦ (More)

We study the inverse problem of determining an electrical inclusion from boundary measurements. We derive a stability estimate for the linearized map with explicit formulae on generic constants thatâ€¦ (More)

In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as theâ€¦ (More)

In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we canâ€¦ (More)

We survey some recent results on the reconstruction of discontinuities by boundary measurements for elasticity and related systems in two dimensions. Our main tool is a new type of complexâ€¦ (More)