9 papers · 1 filter
Improved stability of low Fourier modes in inverse problems for potentials
Tony Liimatainen, William Trad, Mikko Salo
We prove Lipschitz, sub-Hölder and Hölder stability estimates for recovering the low Fourier modes of an unknown potential from the Dirichlet-to-Neumann (DN) map. We study three di…
Reconstruction for an inverse scattering problem with a Kerr type nonlinearity
Khaoula El Maddah, Matti Lassas, Tony Liimatainen +2
We study the inverse scattering problem for the Kerr-nonlinear Helmholtz equation \[ Îu + k^2(1+q(x)|u|^2)u = 0 \quad \text{in }\mathbb{R}^n,\; n\geq 2, \] where the aim is to rec…
An inverse source problem for a quasilinear elliptic equation
Tony Liimatainen, Shubham Jaiswal
We initiate the study of inverse source problems for quasilinear elliptic equations of the form \[ \left\{ \begin{array}{ll} \nabla \cdot (γ(x,u,\nabla u) \nabla u) = F & \text{in…
An Inverse Problem for the Prescribed Mean Curvature
Tony Liimatainen, Janne Nurminen
We extend the recent study of inverse problems for minimal surfaces by considering the inverse source problem for the prescribed mean curvature equation \begin{equation*} \nabla \c…
Generalized boundary rigidity and minimal surface transform
Leonard Busch, Tony Liimatainen, Mikko Salo +1
We study a generalized boundary rigidity problem, which investigates whether the areas of embedded minimal surfaces can uniquely determine a Riemannian manifold with boundary. We p…
An inverse problem for the Monge-Ampère equation
Tony Liimatainen, Yi-Hsuan Lin
We extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Ampère equation \[ \det D^2 u…