Publications

Preprint or accepted manuscript can be found below in pdf form. The final version of these articles can be changed after publication, so please read them in the indicated journals via the [Link]. You can also find my preprints in terms of chronological records via . Besides, you might be interested to see my , , and related to my research outputs.

Preprints/Submitted Papers

25. (with H. Liu and X. Liu) Determining a nonlinear hyperbolic system with unknown sources and nonlinearity
submitted (2021), arXiv:2107.10219.

24. (with P.-Z. Kow and J.-N. Wang) The Calderón problem for the fractional wave equation: Uniqueness and optimal stability
submitted (2021), arXiv:2105.11324.

23. (with T. Liimatainen, M. Salo, and T. Tyni) Inverse problems for elliptic equations with fractional power type nonlinearities
submitted (2020), arXiv:2012.04944.

22. Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities
submitted (2020), arXiv:2005.07163.

21. (with R.-Y. Lai) Inverse problems for fractional semilinear elliptic equations
submitted (2020), arXiv:2004.00549.

Published/Accepted Papers

20. (with P. Caro, R.-Y. Lai and T. Zhou) Boundary determination of electromagnetic and Lamé parameters with corrupted data
Inverse Probl. Imaging, published online (2021), doi: 10.3934/ipi.2021033 .[Link]

19. (with M. Lassas, T. Liimatainen and M. Salo) Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
Rev. Mat. Iberoam., Vol. 37, Issue 4, (2021), 1553–1580. [Link]

18. (with G. Nakamura, R. Potthast and H. Wang) Duality between range and no-response tests and its application for inverse problems
Inverse Probl. Imaging, Vol. 15, No.2 (2021), 367-386. [Link]

17. (with M. Lassas, T. Liimatainen and M. Salo) Inverse problems for elliptic equations with power type nonlinearities
J. Math. Pures Appl., Vol. 145 (2021), 44-82. [Link]

16. (with R. Murthy, K. Shin and J. Mueller) A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón method in the plane
Inverse Problems, Vol 36 (2020), 125008. [Link]

15. (with R.-Y. Lai and A. Rüland) The Calderón problem for a space-time fractional parabolic equation
SIAM J. Math Anal., Vol. 52, Issue 3 (2020), 2655-2688. [Link]

14. (with M. Cekić and A. Rüland) The Calderón problem for the fractional Schrödinger equation with drift
Cal. Var. Partial Differential Equations, Vol. 59, No. 3 (2020), 1-46. [Link]

13. (with B. Harrach) Monotonicity-based inversion of the fractional Schrödinger equation II. General potentials and stability
SIAM J. Math Anal., Vol. 52, Issue 1 (2020), 402-436. [Link]

12. (with B. Harrach) Monotonicity-based inversion of the fractional Schrödinger equation I. Positive potentials
SIAM J. Math Anal., Vol. 51, Issue 4 (2019), 3092-3111. [Link]

11. (with S. Meng) Leading and second order homogenization of an elastic scattering problem for highly oscillating anisotropic medium
J. Elasticity, Vol. 137, Issue 2 (2019), 177-217. [Link]

10. (with X. Cao and H. Liu) Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
Inverse Probl. Imaging, Vol. 13, Issue 1 (2019), 197-210. [Link]

9. (with R.-Y. Lai) Global uniqueness for the fractional semilinear Schrödinger equation
Proc. Amer. Math. Soc. 147 (2019), 1189-1199. [Link]

8. (with E. Blåsten) Radiating and non-radiating sources in elasticity
Inverse Problems, Vol. 35, No. 1 (2018), 1-16. [Link]

7. (with B. Harrach and H. Liu) On localizing and concentrating electromagnetic fields
SIAM J. Appl. Math, 78(5) (2018), 2558-2574. [Link]

6. Nearly cloaking for the elasticity system with residual stress
Asymptot. Anal., Vol. 106, Issue 1 (2018), 1-23. [Link]

5. (with T. Ghosh and J. Xiao) The Calderón problem for variable coefficient nonlocal elliptic operators
Comm. Partial Differential Equations, Vol. 42, No. 12 (2017), 1923-1961. [Link]

4. (with G. Nakamura) Boundary determination of the Lamé moduli for the isotropic elasticity system
Inverse Problems, Vol. 33, No. 12 (2017), 1-23. [Link]

3. Reconstruction of penetrable obstacles in the anisotropic acoustic scatterings
Inverse Probl. Imaging, Vol. 10, Issue 3 (2016), 765-780. [Link]

2. Strong unique continuation for a residual stress system with Gevrey coefficients
Proc. Amer. Math. Soc. 144 (2016), 2171-2183. [Link]

1. (with R. Kuan and M. Sini) The enclosure method for the anisotropic Maxwell system
SIAM J. Math Anal., Vol 47 (2015), 3488-3527. [Link]

Other Articles

◆ (with E. Blåsten) Corrigendum: Radiating and non-radiating sources in elasticity
unpublished manuscript (2021)

Collaborators

Blåsten, Emilia (Freelance mathematician, Helsinki, Finland)

Cao, Xinlin (Research Scientist, Johann Radon Institute for Computational and Applied Mathematics, Austria)

Caro, Pedro (Ikerbasque Research Fellow at BCAM, Spain)

Cekić, Mihajlo (Postdoctoral Fellow, Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, France)

Ghosh, Tuhin (Research Associate, Bielefeld University, Germany)

Harrach, Bastian (Professor, Goethe University Frankfurt, Germany)

Kow, Pu-Zhao (Postdoctoral fellow, Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Kuan, Rulin (Assistant Professor, National Cheng Kung University, Taiwan)

Lai, Ru-Yu (Assistant Professor, University of Minnesota, USA)

Lassas, Matti (Academy Professor, Department of Mathematics and Statistics, University of Helsinki, Finland)

Liimatainen, Tony (Postdoctoral Fellow, Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Liu, Hongyu (Professor, Department of Mathematics, City University of Hong Kong, Hong Kong)

Liu, Xu (Professor, School of Mathematics and Statistics, Northeast Normal University, China)

Meng, Shixu (Associate Professor, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, China)

Muller, Jennifer (Professor, Department of Mathematics, Colorado State University, USA)

Murthy, Rashmi (Postdoctoral Fellow, University of Helsinki, Finland)

Nakamura, Gen (Professor, Hokkaido University, Japan)

Potthast, Roland (Director and Professor for Data Assimilation at DWD/DMVI, Germany & Professor in University of Reading, UK)

Rüland, Angkana (Professor, Institut für Angewandte Mathematik, Ruprecht-Karls Universität Heidelberg, Germany)

Salo, Mikko (Professor, Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Shin, Kwancheol (PhD stduent, Colorado State University, USA)

Sini, Mourad (Professor, Johann Radon Institute for Computational and Applied Mathematics, Austria)

Tyni, Teemu (Postdoctoral Fellow, Department of Mathematics and Statistics, University of Helsinki, Finland)

Wang, Haibing (Professor, Department of Mathematics, Southeast University, China)

Wang, Jenn-Nan (Professor, Institute of Applied Mathematics, National Taiwan University, Taiwan)

Xiao, Jingni (Hill Assistant Professor, Rutgers University, USA)

Zhou, Ting (Associate Professor, Northeastern University, USA)

(in alphabetical order)

PhD Thesis

Download, doi: 10.6342, NTU/201600158
Slide for the PhD thesis defense

Some Lecture Notes

These notes (only for personal records) might be incorrect or contain errors. Please be careful in using them.

◆ Harmonic Analysis course @ NTU, 2016.02-2016.06 PDF

◆ NCTS Distinguished Scholar and NTU visiting chair
     - Spectral Graph Theory and its Applications PDF

◆ IAS workshop on Inverse Problems, Imaging and PDE
     - Calderon's problem for elliptic system PDF

◆ NCTS Summer Courses on Analysis and PDEs
     - Introduction to EIT PDF
     - Classical DeGiorgi method to NS equation PDF

◆ NCTS Minicourse on Periodic Homogenization of Elliptic Problems
     - Introduction to elliptic homogenization problem PDF

◆ NCTS seminar - The DeGiorgi method and its application to parabolic regularity
     - Vasseur, DeGiorgi method PDF

◆ On the inviscid limit problem for incompressible flows in the half-plane
     - Incompressible Navier-Stokes equation PDF

◆ NCTS Distinguished Lectures Series (Click Here)
     - Theory and Applications to homogenization - A revisit with recent progress PDF

◆ Other Notes:
     - Method of moving plane PDF
     - Dirichlet-Neumann relations PDF
     - Radon transform PDF
     - Liapunov-Schmidt reduction PDF