陈虎元

个人简介

陈虎元， 主要研究领域是半线性椭圆和抛物线方程的解的性质，椭圆算子的特征值等性质。 具体来说，我的兴趣是：

• 非线性椭圆方程的Liouville定理。 这里包括完全非线性算子、Hardy-Leray算子和非局部算子，特别是分数拉普拉斯算子，在各种类型的域中。
• 半线性爆破解和分布解的研究， 带有测量源的椭圆和抛物线方程。
• 椭圆算子的基本性质，算子表达和基本解。 其中退化算子有二阶Hardy算子，分数阶Hardy算子。 此外，还包括一类极端算子，如对数阶算子，其傅立叶变换为2 log|·|。

教育经历

• 2014.1 博士毕业于智利大学和法国图尔大学，获得双博士学位。

工作经历

• 2014.08-2025.06   Jiangxi Normal University   Professor (2023)
• 2014.08-2016.07 上海纽约大学，博士后
• 2019.01-2019.10   德国法兰克福歌德大学，博士后
• 2023.12-2024.11  悉尼大学， 访问学者

荣誉和获奖

2019年获得洪堡学者基金
2021年入选江西省“青年井冈学者”奖励计划，
2022年以独立完成人身份获江西省自然科学奖二等奖

论著

• 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).