The Calderón Problem for the Fractional Wave Equation: Uniqueness and Optimal Stability
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Publication:5084115
DOI10.1137/21M1444941zbMath1492.35427arXiv2105.11324MaRDI QIDQ5084115
Yi-Hsuan Lin, Pu-Zhao Kow, Jenn-Nan Wang
Publication date: 23 June 2022
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.11324
fractional Laplacianperidynamicsstrong uniquenesslogarithmic stabilityRunge approximationexterior Dirichlet-to-Neumann map
Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Inverse problems for PDEs (35R30) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
- Hitchhiker's guide to the fractional Sobolev spaces
- Ten equivalent definitions of the fractional Laplace operator
- Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map
- Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
- Completeness of products of solutions and some inverse problems for PDE
- On continuous dependence for an inverse initial boundary value problem for the wave equation
- Some observations on the Green function for the ball in the fractional Laplace framework
- An inverse problem for the wave equation
- Functional analysis, Sobolev spaces and partial differential equations
- Unique continuation for fractional orders of elliptic equations
- Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
- Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
- The fractional Calderón problem: low regularity and stability
- Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
- The Calderón problem for the fractional Schrödinger equation with drift
- Well-posedness results for fractional semi-linear wave equations
- Determining a fractional Helmholtz equation with unknown source and scattering potential
- Strong unique continuation for the higher order fractional Laplacian
- The Calderón problem for the fractional Schrödinger equation
- Unique determination of a time-dependent potential for wave equations from partial data
- Exponential instability in an inverse problem for the Schrödinger equation
- Stability For a Multidimensional Inverse Spectral Theorem
- Increasing stability of the inverse boundary value problem for the Schr\"odinger equation
- Uniqueness for an inverse problem for the wave equation
- Examples of exponential instability for inverse inclusion and scattering problems
- The Calderón problem for variable coefficients nonlocal elliptic operators
- Exponential instability in the fractional Calderón problem
- Global uniqueness for the fractional semilinear Schrödinger equation
- Stable determination of conductivity by boundary measurements
- Optimality of Increasing Stability for an Inverse Boundary Value Problem
- The Calderón Problem for a Space-Time Fractional Parabolic Equation
- Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit
- Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability
- Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials
- Unique Continuation for Fractional Schrödinger Equations with Rough Potentials
- Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
- An Extension Problem Related to the Fractional Laplacian
- Inverse Hyperbolic Problems with Time-Dependent Coefficients
- A new approach to hyperbolic inverse problems
- Determination of time-dependent coefficients for a hyperbolic inverse problem
- Inverse problems for the fractional-Laplacian with lower order non-local perturbations
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