On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols

DOI10.1016/j.jde.2022.09.009zbMath1504.35643arXiv2109.14976OpenAlexW4296534451MaRDI QIDQ2109351

Giovanni Covi, M. Ángeles García-Ferrero, Angkana Rüland

Publication date: 21 December 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.14976

zbMATH Keywords

inverse problemnonlocal operatorsdirectional antilocalitydomain-of-dependence formulation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Partial functional-differential equations (35R10) Integro-differential operators (47G20)

Related Items (3)

Fractional Calderón problems and Poincaré inequalities on unbounded domains ⋮ On (global) unique continuation properties of the fractional discrete Laplacian ⋮ Singular integrals and Feller semigroups with jump phenomena

Uses Software

• DLMF

Cites Work

• Unnamed Item
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• Nonlocal diffusion and applications
• Regularity theory for general stable operators
• Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
• Graph properties for nonlocal minimal surfaces
• Is a nonlocal diffusion strategy convenient for biological populations in competition?
• All functions are locally \(s\)-harmonic up to a small error
• Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map
• Regularity of harmonic functions for a class of singular stable-like processes
• Regularity results for stable-like operators
• On some partial data Calderón type problems with mixed boundary conditions
• The \(\Gamma\)-antilocality of stable generators whose Lévy measures are supported on a cone
• Antilocality and one-sided antilocality for stable generators on the line
• Remarks on transmission, antitransmission and antilocal properties for sums of stable generators
• Martin boundary and integral representation for harmonic functions of symmetric stable processes
• Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
• Censored stable processes
• Fractional quantum mechanics and Lévy path integrals
• Can one see \(\alpha\)-stable variables and processes?
• Unique continuation for fractional orders of elliptic equations
• Harnack's inequality for stable Lévy processes
• Unique continuation for sublinear elliptic equations based on Carleman estimates
• Lévy flights and related topics in physics. Proceedings of the international workshop, held at Nice, France, 27-30 June, 1994
• Inverse problems for a fractional conductivity equation
• The fractional Calderón problem: low regularity and stability
• Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
• On an inverse problem for a fractional semilinear elliptic equation involving a magnetic potential
• Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
• Inverse problems for fractional semilinear elliptic equations
• Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
• A non-local inverse problem with boundary response
• The higher order fractional Calderón problem for linear local operators: uniqueness
• Non-symmetric stable operators: regularity theory and integration by parts
• 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
• Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data
• The Dirichlet problem for nonlocal operators
• Antilocality and a Reeh-Schlieder theorem on manifolds
• Regularity for the Boltzmann equation conditional to macroscopic bounds
• Nonlocal quadratic forms with visibility constraint
• Integro-Differential equations with nonlinear directional dependence
• Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
• Nonlocal Continuum Field Theories
• Nonlocal Operators with Applications to Image Processing
• Bemerkungen zur unitäräquivalenz von lorentzinvarianten feldern
• On Single Measurement Stability for the Fractional Calderón Problem
• Euler Equations, Navier-Stokes Equations and Turbulence
• Electrical impedance tomography and Calderón's problem
• Recovering a function from a finite number of moments
• The Calderón problem for variable coefficients nonlocal elliptic operators
• Exponential instability in the fractional Calderón problem
• PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES
• A continuous dependence result in the analytic continuation problem
• Microlocal analysis of quantum fields on curved space–times: Analytic wave front sets and Reeh–Schlieder theorems
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• Null-control and measurable sets
• On two methods for quantitative unique continuation results for some nonlocal operators
• An inverse problem for the fractional Schrödinger equation in a magnetic field
• Determining the magnetic potential in the fractional magnetic Calderón problem
• The Calderón Problem for a Space-Time Fractional Parabolic Equation
• Regularity of harmonic functions for anisotropic fractional Laplacians
• Nonlocal operators with singular anisotropic kernels
• 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
• On shape optimization problems involving the fractional laplacian
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• On unique continuation for Schrödinger operators of fractional and higher orders
• A representation theorem for symmetric stable processes and stable measures on H
• Inverse problems for the fractional-Laplacian with lower order non-local perturbations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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