10 papers
Fractional Calderón problem with -conductivities
Gunther Uhlmann, Philipp Zimmermann
We study the inverse problem for the fractional conductivity equation with uniformly elliptic conductivities . For every and , we prove…
Recovery of Rough Sources in the Inverse Monge--Ampère Problem
Gunther Uhlmann, Philipp Zimmermann
We prove that every nonnegative source \(f\in L^1(Ω)\) in the Monge--Ampère equation \[ \det D^2u=f\quad\text{in }Ω, \] on a bounded uniformly convex \(C^{1,1}\) domain \(Ω\subset\…
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 bo…
Inverse Problems for the Monge-Ampère Equation: Linearization and Nonlinear Recovery
Gunther Uhlmann, Philipp Zimmermann
We study inverse boundary value problems for the fully nonlinear Monge-Ampère equation in a bounded domain. Motivated by Calderón-type problems, we in…
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 extend…
The Calderón problem for the Schrödinger equation in transversally anisotropic geometries with partial data
Yi-Hsuan Lin, Gen Nakamura, Philipp Zimmermann
We study the partial data Calderón problem for the anisotropic Schrödinger equation \begin{equation} \label{eq: a1} (-Δ_{\widetilde{g}}+V)u=0\text{ in }Ω\times (0,\infty), \end{equ…
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…
Approximation and uniqueness results for the nonlocal diffuse optical tomography problem
Yi-Hsuan Lin, Philipp Zimmermann
We investigate the inverse problem of recovering the diffusion and absorption coefficients in the nonlocal diffuse optical tomography equation $(-\text{div}( σ\nabla))^s u+…
Well-posedness and inverse problems for semilinear nonlocal wave equations
Yi-Hsuan Lin, Teemu Tyni, Philipp Zimmermann
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results…
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 de…