## 38 Citations

### Uniqueness results for inverse source problems of semilinear elliptic equations

- Mathematics
- 2022

. We study inverse source problems associated to semilinear elliptic equations of the form ∆ u ( x ) + a ( x,u ) = F ( x ) , on a bounded domain Ω ⊂ R n , n ≥ 2. Unlike inverse source problems for…

### GLOBAL UNIQUENESS FOR SEMILINEAR EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN

- Mathematics
- 2022

In this article we investigate inverse problems of heat and wave equations involving fractional Laplacian operator with zeroth order nonlinear perturbations. The study of inverse problems involving…

### The global inverse fractional conductivity problem

- Mathematics
- 2022

. We prove global uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and…

### Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems

- MathematicsInverse Problems & Imaging
- 2021

We prove a unique continuation property for the fractional Laplacian $(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we study Poincar\'e-type inequalities for the operator…

### An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds

- Mathematics
- 2021

Given a conformally transversally anisotropic manifold (M, g), we consider the semilinear elliptic equation (−∆g + V )u+ qu 2 = 0 on M. We show that an a priori unknown smooth function q can be…

### Inverse problems for fractional equations with a minimal number of measurements

- Mathematics
- 2022

. In this paper, we study several inverse problems associated with a fractional diﬀerential equation of the following form: which is given in a bounded domain Ω ⊂ R n , n ≥ 1. For any ﬁnite N , we…

### The Calderón Problem for the Fractional Wave Equation: Uniqueness and Optimal Stability

- MathematicsSIAM J. Math. Anal.
- 2022

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues…

### Simultaneous recoveries for semilinear parabolic systems

- Mathematics
- 2021

In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish…

### The fractional $p\,$-biharmonic systems: optimal Poincar\'e constants, unique continuation and inverse problems

- Mathematics
- 2022

. This article investigates nonlocal, fully nonlinear generalizations of the classical biharmonic operator ( − ∆) 2 . These fractional p -biharmonic operators appear naturally in the variational…

### The higher order fractional Calderón problem for linear local operators: Uniqueness

- MathematicsAdvances in Mathematics
- 2022

## References

SHOWING 1-10 OF 30 REFERENCES

### Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations

- Mathematics
- 2019

We study various partial data inverse boundary value problems for the semilinear elliptic equation $\Delta u+ a(x,u)=0$ in a domain in $\mathbb R^n$ by using the higher order linearization technique…

### The Calderón Problem for a Space-Time Fractional Parabolic Equation

- MathematicsSIAM J. Math. Anal.
- 2020

This article uniquely determine the unknown bounded potential $Q$ from infinitely many exterior Dirichlet-to-Neumann type measurements based on Runge approximation and the dual global weak unique continuation properties of the equation under consideration.

### An inverse problem for a semi-linear elliptic equation in Riemannian geometries

- MathematicsJournal of Differential Equations
- 2020

### The Calderón problem for the fractional Schrödinger equation with drift

- Mathematics
- 2020

We investigate the Calderon problem for the fractional Schrodinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely…

### The Calderón problem for variable coefficients nonlocal elliptic operators

- Mathematics
- 2017

ABSTRACT In this paper, we introduce an inverse problem of a Schrödinger type variable nonlocal elliptic operator (−∇⋅(A(x)∇))s+q), for 0<s<1. We determine the unknown bounded potential q from the…

### The Calderón problem for the fractional Schrödinger equation

- Mathematics
- 2016

We show global uniqueness in an inverse problem for the fractional Schrodinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also…

### Global uniqueness for the fractional semilinear Schrödinger equation

- MathematicsProceedings of the American Mathematical Society
- 2018

We study global uniqueness in an inverse problem for the fractional semilinear Schrödinger equation (−∆)su + q(x, u) = 0 with s ∈ (0, 1). We show that an unknown function q(x, u) can be uniquely…

### Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities

- Mathematics
- 2019

We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega\subset \mathbb{R}^n$ which vanish on a closed proper subset of the…

### Monotonicity-based inversion of the fractional Schr\"odinger equation

- Mathematics
- 2017

We consider the inverse problems of for the fractional Schr\"{o}dinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials…