Huyuan Chen

Bio

My research interests focus on the qualitative properties of solutions to linear and nonlinear differential equations.  Specifically, I am interested in:

• Liouville Theorems for semilinear elliptic equations involving fully nonlinear operators, Hardy-Leray operators, and nonlocal operators, particularly the fractional Laplacian, in various types of domains.
• The study of blow-up solutions and distributional solutions of semilinear elliptic and parabolic equations with measure sources.
• The properties of elliptic operators, such as the eigenvalues and fundamental solutions. Here the elliptic operator including Hardy operators coupled with the Laplacian or fractional Laplacian. Additional, I am also interested in some extremal soltuions. such that the logarithmic Laplacian   whose Fourier transforms is 2 log |·|.

Education Experience

• In 2014   two doctoral degrees from the University of Chile and the University of Tours in France.

Work Experience

• 2014.08-2025.06   Jiangxi Normal University   Professor (2023)
• 2014.08-2016.07   NYU Shanghai       post-doc
• 2019.01-2019.10   Goethe University Frankfurt  post-doc
• 2023.12-2024.11  The University of Sydney     post-doc

Honors and Awards

In 2019    Humboldt Scholar Fund
In 2021    The “Young Jinggang Scholars” Award Program in Jiangxi Province
In 2022    The second prize of Jiangxi Provincial Natural Science Award

Publications

• Huyuan Chen and Tobias Weth, The Dirichlet Problem for the Logarithmic Laplacian, Communications in Partial Differential Equations, 44, 1100-1139 (2019).
•    Huyuan Chen, Liouville theorem for the fractional Lane-Emden equation in an unbounded domain, Journal de Mathematiques Pures et Appliquees, 111, 21-46 (2018).
•    Huyuan Chen, Patricio Felmer and Jianfu Yang, Weak solutions of semilinear elliptic equation involving Dirac mass, Annales de l Institut Henri Poincare-Analyse Non Lineaire, 35, 729-750 (2018).
•    Huyuan Chen, Patricio Felmer and Alexander Quaas, Large solutions to elliptic equations involving fractional Laplacian, Annales de l Institut Henri Poincare-Analyse Non Lineaire, 32, 1199-1228 (2015).
•    Huyuan Chen, Hichem Hajaiej, Ying Wang, Liouville theorem for semilinear elliptic inequalities with the fractional Hardy operators, Transactions of the American Mathematical Society, 378(1) 339-374 (2025).
•    Huyuan Chen and Tobias Weth, The Poisson problem for the fractional Hardy operator: Distributional identities and singular solutions, Transactions of the American Mathematical Society, 374(10), 6881-6925 (2021).
•    Huyuan Chen and Laurent Veron, The Cauchy problem associated to the logarithmic Laplacian with an application to the fundamental solution, Journal of Functional Analysis, 287, No 110470, 72 pages (2024).
•    Huyuan Chen, Hichem Hajaiej and Laurent Veron, Qualitative properties of solutions to semilinear elliptic equations from the gravitational Maxwell Gauged O(3) Sigma model, Journal of Functional Analysis, 282(7), 109379 (2022).
•    Huyuan Chen and Laurent Veron, Initial trace of positive solutions to fractional diffusion equations with absorption, Journal of Functional Analysis, 276(4), 1145-1200 (2019).
•    Huyuan Chen and Laurent Veron, Semilinear fractional elliptic equations with gradient nonlinearity involving measures, Journal of Functional Analysis, 266(8), 5467-5492 (2014).
•    Huyuan Chen and Alexander Quaas, Classification of isolated singularities of nonnegative solutions to fractional semilinear elliptic equations and the existence results, Journal of the London Mathematical Society, 97(2), 196-221 (2018).
•    Huyuan Chen, Gilles Evequoz and Tobias Weth, Complex Solutions and Stationary Scattering for the Nonlinear Helmholtz Equation, SIAM Journal on Mathematical Analysis, 53(2), 2349-2372 (2021).
•    Huyuan Chen, Rui Peng and Feng Zhou, Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain, Science China-Mathematics, 63(7), 1307-1322 (2020).
•    Huyuan Chen and Laurent Veron, Singularities of fractional Emden’s equations via Caffarelli-Silvestre extension, Journal of Differential Equations, 361, 472-530 (2023).
•   Huyuan Chen, Mousomi Bhakta and Hichem Hajaiej, On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians, Journal of Differential Equations, 317, 1-31 (2022).
•   Huyuan Chen and Laurent Veron, Schrodinger operators with Leray-Hardy potential singular on the boundary, Journal of Differential Equations, 269(3), 2091-2131 (2020).
•   Huyuan Chen and Feng Zhou, Classification of isolated singularities of positive solutions for Choquard equations, Journal of Differential Equations, 261, 6668-6698 (2016).
•   Huyuan Chen and Laurent Veron, Semilinear fractional elliptic equations involving measures, Journal of Differential Equations, 257(5), 1457-1486 (2014).   Huyuan Chen and Patricio Felmer, On the Liouville Property for fully nonlinear equations with gradient term, Journal of Differential Equations, 255, 2167-2195 (2013).