5 papers
An Inverse Obstacle Problem for the Fractional Schrödinger Equation
Gunter Uhlmann, Philipp Zimmermann
We study an inverse obstacle problem for the fractional Schrödinger operator , . For each exterior datum, the state is constrained by a prescribed obstacle in a…
Inverse Problems for the Monge--Ampère Equation: Linearization and Nonlinear Recovery
Gunther Uhlmann, Philipp Zimmermann
We study inverse boundary value problems for the nonlinear Monge--Ampère equation \[ \det D^2u=a(x,u,\nabla u) \] in a bounded domain. We introduce a nonlinear Cauchy data set and…
Calderón problem for nonlocal viscous wave equations: Unique determination of linear and nonlinear perturbations
Philipp Zimmermann
The main goal of this article is to study a Calderón type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely d…
Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities
Yi-Hsuan Lin, Teemu Tyni, Philipp Zimmermann
The main purpose of this article is to establish the Runge-type approximation in for solutions of linear nonlocal wave equations. To achieve this, we…
Optimal Runge approximation for damped nonlocal wave equations and simultaneous determination results
Philipp Zimmermann
The main purpose of this article is to establish new uniqueness results for Calderón type inverse problems related to damped nonlocal wave equations. To achieve this goal we exten…