15 citations · 77 across the 31 of their papers we have counts for
37 papers
Density of Products of Solutions and the Linearized Calderón Problem in an Analytic Background
Leonard Busch, Tony Liimatainen, Gunther Uhlmann
We study the linearization, with respect to zeroth-order perturbations, of the local Dirichlet-to-Neumann map of a formally self-adjoint elliptic operator on a compact R…
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 \[ Δu + k^2(1+q(x)|u|^2)u = 0 \quad \text{in }\mathbb{R}^n,\; n\geq 2, \] where the aim is to reco…
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…
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 prove uniqueness for an inverse source problem for the Monge--Ampère equation on a bounded uniformly convex planar domain. The source is smooth and strictly positi…
Gaussian beam interactions and inverse source problems for nonlinear wave equations
Matti Lassas, Tony Liimatainen, Valter Pohjola +1
We study the inverse source problem for the semilinear wave equation \[ (\Box_g + q_1)u + q_2 u^2 = F, \] on a globally hyperbolic Lorentzian manifold. We demonstrate that the coef…
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…
Bulk metric reconstruction from entanglement data via minimal surface area variations
Niko Jokela, Tony Liimatainen, Miika Sarkkinen +1
We investigate the reconstruction of asymptotically anti-de Sitter (AdS) bulk geometries from boundary entanglement entropy data for ball-shaped entangling regions. By deriving an…
The Calderón problem on Riemannian surfaces and of minimal surfaces
Cătălin I. Cârstea, Tony Liimatainen, Leo Tzou
In this paper we prove two results. The first shows that the Dirichlet-Neumann map of the operator on a Riemannian surface can determine its topological, differential, and…
Applications of the Stone-Weierstrass theorem in the Calderón problem
Tony Liimatainen, Mikko Salo
We give examples on the use of the Stone-Weierstrass theorem in inverse problems. We show uniqueness in the linearized Calderón problem on holomorphically separable Kähler manifold…
An inverse problem for general minimal surfaces
Cătălin I. Cârstea, Matti Lassas, Tony Liimatainen +1
In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if is a -dimensio…
Calderón problem for the quasilinear conductivity equation in dimension
Tony Liimatainen, Ruirui Wu
In this paper we prove a uniqueness result for the Calderón problem for the quasilinear conductivity equation on a bounded domain . The proof of the result is based on the hi…
On determining and breaking the gauge class in inverse problems for reaction-diffusion equations
Yavar Kian, Tony Liimatainen, Yi-Hsuan Lin
We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equati…
Uniqueness results and gauge breaking for inverse source problems of semilinear elliptic equations
Tony Liimatainen, Yi-Hsuan Lin
We study inverse source problems associated to semilinear elliptic equations of the form \[ Δu(x)+a(x,u)=F(x), \] on a bounded domain , . We show th…
An inverse problem for a semi-linear wave equation: a numerical study
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado +1
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in dimensions. We develop a numerical schem…
An inverse problem for the Riemannian minimal surface equation
Cătălin I. Cârstea, Matti Lassas, Tony Liimatainen +1
In this paper we consider determining a minimal surface embedded in a Riemannian manifold . We show that if is a two dimensional Riemannian manifold with bo…
An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds
Ali Feizmohammadi, Tony Liimatainen, Yi-Hsuan Lin
Given a conformally transversally anisotropic manifold , we consider the semilinear elliptic equation We show that an a priori unk…
Stability estimates for inverse problems for semi-linear wave equations on Lorentzian manifolds
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado +1
This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold.…
Counterexamples to inverse problems for the wave equation
Tony Liimatainen, Lauri Oksanen
We construct counterexamples to inverse problems for the wave operator on domains in , , and on Lorentzian manifolds. We show that non-isometric Lorentzi…
Inverse problems for elliptic equations with fractional power type nonlinearities
Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo +1
We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps…
An Inverse Problem for the Relativistic Boltzmann Equation
Tracey Balehowsky, Antti Kujanpää, Matti Lassas +1
We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime with an unknown metric . We consider measurements done in a neigh…
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds
Katya Krupchyk, Tony Liimatainen, Mikko Salo
In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmo…
Uniqueness and stability of an inverse problem for a semi-linear wave equation
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado +1
We consider the recovery of a potential associated with a semi-linear wave equation on , . We show a Hölder stability estimate for the recovery of an unk…