The Calderón Problem for a Space-Time Fractional Parabolic Equation

DOI10.1137/19M1270288zbMath1447.35382arXiv1905.08719OpenAlexW3033591361MaRDI QIDQ5119981

Ru-Yu Lai, Angkana Rüland, Yi-Hsuan Lin

Publication date: 9 September 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.08719

zbMATH Keywords

Carleman estimateunique continuation propertyRunge approximationfractional parabolic Calderón problemexterior Dirichlet-to-Neumann measurements

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Inverse problems for PDEs (35R30) Initial value problems for PDEs with pseudodifferential operators (35S10) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• All functions are locally \(s\)-harmonic up to a small error
• Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
• Completeness of products of solutions and some inverse problems for PDE
• Global uniqueness in an inverse problem for time fractional diffusion equations
• Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations
• Limit theorems for coupled continuous time random walks.
• Stability of the determination of a time-dependent coefficient in parabolic equations
• The influence of a line with fast diffusion on Fisher-KPP propagation
• The fractional Calderón problem: low regularity and stability
• Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
• Quantitative approximation properties for the fractional heat equation
• The Calderón problem for the fractional Schrödinger equation with drift
• Quantitative invertibility and approximation for the truncated Hilbert and Riesz transforms
• Strong unique continuation for the higher order fractional Laplacian
• The Calderón problem for the fractional Schrödinger equation
• Local density of solutions to fractional equations
• Higher regularity for the fractional thin obstacle problem
• Local approximation of arbitrary functions by solutions of nonlocal equations
• Determining Coefficients in a Class of Heat Equations via Boundary Measurements
• A stability result for a time-dependent potential in a cylindrical domain
• Random Walks on Lattices. II
• Some stability estimates in determining sources and coefficients
• The Calderón problem for variable coefficients nonlocal elliptic operators
• Exponential instability in the fractional Calderón problem
• Global uniqueness for the fractional semilinear Schrödinger equation
• Space-time fractional derivative operators
• Global uniqueness of a multidimensional inverse problem for a nonlinear parabolic equation by a Carleman estimate
• Microlocal analysis of quantum fields on curved space–times: Analytic wave front sets and Reeh–Schlieder theorems
• Local density of Caputo-stationary functions of any order
• Inverse problems: seeing the unseen
• Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability
• Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials
• A tutorial on inverse problems for anomalous diffusion processes
• Unique Continuation for Fractional Schrödinger Equations with Rough Potentials
• Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients
• Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem
• Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation
• Inverse acoustic and electromagnetic scattering theory
• Inverse problems for partial differential equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach