孙玉华

2004.09-2008.07 吉林大学数学学院 本科

2008.09-2013.01 清华大学数学系 博士

2011.09-2014.07 德国比勒菲尔德大学数学系 博士

2016.12-至今  南开大学数学学院 副教授

2014.10-2016.12 南开大学数学学院 讲师

流形与加权图上的分析和偏微分方程

本科生课程：高等代数与解析几何，数学分析，高等数学，常微分方程，数理方程，变分学。

研究生课程：偏微分方程。

主持的科研项目：

1. 国家自然科学基金青年科学基金项目：“黎曼流形上椭圆微分不等式非负解的唯一性及其相关问题的研究”，21.16万元，No.11501303, 2016.01-2018.12。

2. 教育部留学人员回国启动基金项目：“黎曼流形上积分型体积增长估计与微分不等式解的唯一性研究”，3万元，2015.01-2017.12。

3. 教育部高校基本科研业务费：“外区域上抛物型微分不等式的研究”，12万元，2016.01.-2017.12。

4. 南开大学百名青年学科带头人培养计划：“黎曼流形上微分不等式解的研究”，50万元， 2014.12-2020.12。

5. 天津市青年科学基金：“黎曼流形上带位势项非线性抛物方程及其相关问题的研究”， 6万元， 2019.04-2022.03。

6. 国家自然科学基金面上项目：“几类非线性椭圆问题在黎曼流形和加权图上的研究”，43.5万，No. 12371206，2024.01-2027.12

参与的科研项目：

1. 国家自然科学基金国际(地区)合作与交流项目：“函数空间实变理论及其应用”，主持人：北京师范大学杨大春教授，180万元，No.11761131002, 2018.01.01-2020.12.31。

2. 国家自然科学基金面上项目：“分形集上的热核及某些微分不等式”，主持人：清华大学胡家信教授，54万元，No11871296,2019.01-2022.12。

1.Liouville-type laws for quasilinear equations with absorption or source, submitted. (with W. Li, J. Xiao)

2.Sharp criteria for system of elliptic differential inequalities on manifolds, submitted. (with D. Ye, Y. Zheng)

3.Sharp criteria for nonlocal elliptic inequalities on manifolds, arXiv: 2304.02808, submitted.(with Q. Gu, X. Huang)

4.On positive solutions of biharmonic elliptic inequalities on Riemannian manifolds, arXiv:2206.05489, submitted.(with Y. Zheng)

5.A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms, to appear in Journal d'Analyse Mathematique. (with R. Filippucci, Y. Zheng)

6.Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs, Discrete Contin. Dyn. Syst. Ser. S16(2023), no.6, 1484-1516. (with L. Hao)

7.Higher order evolution inequalities with convection terms in an exterior domain of R^N, J. Math. Anal. Appl. Volume 519, Issue 1, 1 March 2023, 126738. (with M. Jleli, B. Samet)

8.On existence and nonexistence of nonnegative solutions to heat equation on Riemannian manifolds, to appear in Geometric Potential Analysis - AAG 6, De Gruyter. (with F. Xu)

9.Semi-linear elliptic inequalities on weighted graphs, Calc. Var. PDEs.,62, 42(2023). (with Q. Gu, X. Huang)

10.Quasilinear Laplace Equations and Inequalities with Fractional Orders,Math. Ann., Vol. 388(2024), 1-60. (with L. Liu, J. Xiao)

11.A sharp Liouville principle for $\Delta_mu+u^p|\nabla u|^q\le 0$ on geodesically complete noncompact Riemannian manifolds, Math. Ann. 384 (2022), Vol. 384, 1309–1341. (with J. Xiao, F. Xu)

12.ed. A. Grigor'yan, Y. Sun, Analysis and partial differential equations on manifolds, fractals and graphs, de Gruyter series Advances in Analysis and Geometry 3, 2021. https://www.degruyter.com/view/title/578846?language=en

13.On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds, Advances in Analysis and Geometry 3, de Gruyter.(with F. Xu)

14.Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold,  Calc. Var. PDEs 59,Article number:170(2020). (with Q. Gu, J. Xiao, F. Xu)

15.Superlinear elliptic inequalities on manifolds, J. Func. Anal. 278(2020), no. 9, 108444.(with A. Grigor’yan, I. Verbitsky)

16.On positive solutions of semilinear elliptic inequalities on Riemannian manifolds, Calc. Var. PDEs. 58(2019),no. 6, Art.207, 30pp.(with A. Grigor’yan)

17.Liouville type theorems forsystems of elliptic differential inequalities on Riemannian manifolds, J. Math. Anal. Appl. Vol. 466(2018), No.1, 426-446.(with F. Xu, L. Wang)

18.Absence of positive solutions to the system of differential inequalities on manifolds, J. Math. Phys. 59(2018), 011510.

19.Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of R^n, Pacific J. Math, Vol. 293 (2018), No. 1, 245–256.

20.Absence of nonnegative solutions to the system of differential inequalities on manifolds, J. Math. Anal. Appl.,450(2017), no. 2, 901–914.

21.The absence of global positive solutions to semilinear parabolic differential inequalities in exterior domain, Proc. Amer. Math. Soc. 145 (2017), no. 8, 3455–3464.

22.Uniqueness result on nonnegative solutions of a large class of differential inequalities on Riemannian manifolds. Pacific J. Math. 280 (2016), no. 1, 241–254.

23.On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds. Comm. Pure Appl. Anal. 14 (2015), no. 5, 1743–1757.

24.On nonexistence of positive solutions of quasi-linear inequality on Riemannian manifolds. Proc. Amer. Math. Soc. 143 (2015), no. 7, 2969–2984.

25.Uniqueness result for non-negative solutions of semi-linear inequalities on Riemannian manifolds. J. Math. Anal. Appl. 419 (2014), no. 1, 643–661.

26.On non-negative solutions of the inequality ∆u+u^σ≤0 on Riemannian manifolds, Comm. Pure Appl. Math., Vol.67(2014), Issue. 8, 1336-1352.(with A.Grigor'yan)

27.Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 5, 1003–1025.(with K.J.Falconer, J. Hu)

28.Heat flow method for Lichnerowicz type equations on closed manifolds, Z. Angew. Math. Phys. 63 (2012), no. 2, 261–270.(with L. Ma, X. Tang)

受邀国内国外学术报告:

2024

2024.01.19-01.21，非线性分析及应用青年学者论坛，浙江师范大学。

2023

2023.04.14-04.17，椭圆与偏微分方程与变分法青年学者论坛，深圳大学。

2023.12.01-12.04，广州青年几何分析研讨会，中山大学，广州。

2022

2022.03.20-03.24，Online Seminar hosted by Hokkaido University, 日本。

2022.06.18-06.19，非线性偏微分方程理论西安研讨会，西安。

2022.06.29-06.30，非线性偏微分方程理论及应用”国际学术会议，黄淮学院。

2022.08.10-08.11，偏微分方程与几何分析研讨会，哈尔滨工业大学。

2022.09.17-09.18， 非线性泛函分析青年学术论坛, 中南大学，北京师范大学, 中国科学院精密测量科学与技术创新研究院联合举办。

2022.11.05-11.06, 偏微分方程青年学者研讨会, 华东师范大学。

2022.11.04-11.06，椭圆方程与相关课题学术研讨会，华南师范大学。

2021

2021.05.04，Online Geometric Analysis Seminar hosted by University of Bielefeld，德国。

2021.10.11-10.15，CIRM Conference Nonlinear Elliptic and Parabolic PDEs , Levico Terme (Trento)，意大利。

2021.12.08-12.10，Ghent-HUFT online Workshop。

2021.12.16-12.20，厦门非线性椭圆偏微分方程研讨会, 厦门大学。

2020

2020.08.24，Online Seminar for Korea Institute For Advanced Study，韩国。

2020.10.30-11.01，Workshop on Nonlinear Partial Differential Equations IX，上海交通大学。

2020.12.16-12.18，椭圆与抛物偏微分方程研讨会，中国科技大学，合肥。

2019

2019.06.02-06.05，Workshop on Bourgain-Demeter Decoupling Method, 天津。

2019.09.23-09.26， International Conference on Analysis and PDEs on Manifolds and Fractals, 天津。

2019.09.30-10.04，International Conference on Function Spaces and Geometric Analysis and Their Applications, 天津。

2019.11.16，方程与几何分析研讨会, 湖北民族大学，恩施。

2019.11.23-24，几何与复分析研讨会，清华大学，北京。

2019.12.06-12.09，加拿大数学会冬季会议，多伦多，加拿大。

2018

2018.04.14-04.15，清华大学基础数学青年论坛, 清华大学。

2018.06.01-06.04， 加拿大数学会夏季会议， Fredericton, New Brunswick, 加拿大。

2018.07.05-07.09，The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taiwan，China.

2017

2017.09.21-23，International Conference on Analysis and PDEs on Manifolds，天津。

2017.10.20-10.22， 第三届微分几何与微分方程会议，中国人民大学，北京。

2016

2016.07.11-07.16, International Conference “Heat Kernels and Analysis on Manifolds and Fractals”, Bielefeld, Germany.

2013

2013.07.15-07.19, Conference“Stochastics and Real World Models 2013”, Bielefeld, Germany.

2012

2012.10.15-10.18, Conference“Stochastics and Real World Models: Recent Progress and New Frontier”,Xuzhou, China.

入选2017年度“131”天津创新型人才第三层次人选，2022年获得天津市数学与统计学联合学术年会“青年学者奖”，2022，2023年度尚格奖教金。

代表作；

1.Sharp criteria for nonlocal elliptic inequalities on manifolds, arXiv: 2304.02808, submitted.(with Q. Gu, X. Huang)

2.A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms, to appear in Journal d'Analyse Mathematique. (with R. Filippucci, Y. Zheng)

3.Quasilinear Laplace Equations and Inequalities with Fractional Orders,Math. Ann., Vol. 388(2024), 1-60. (with L. Liu, J. Xiao)

4.Semi-linear elliptic inequalities on weighted graphs, Calc. Var. PDEs.,62, 42(2023). (with Q. Gu, X. Huang)

5.A sharp Liouville principle for $\Delta_mu+u^p|\nabla u|^q\leq0$ on geodesically complete noncompact Riemannian manifolds, Math. Ann. 384 (2022), Vol. 384, 1309–1341. (with J. Xiao, F. Xu)

6.Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold,  Calc. Var. PDEs 59,Article number:170(2020). (with Q. Gu, J. Xiao, F. Xu)

7.Superlinear elliptic inequalities on manifolds, J. Func. Anal. 278(2020), no. 9, 108444.(with A. Grigor’yan, I. Verbitsky)

8.On positive solutions of semilinear elliptic inequalities on Riemannian manifolds, Calc. Var. PDEs. 58(2019),no. 6, Art.207, 30pp.(with A. Grigor’yan)

9.Uniqueness result for non-negative solutions of semi-linear inequalities on Riemannian manifolds. J. Math. Anal. Appl. 419 (2014), no. 1, 643–661.

10.On non-negative solutions of the inequality ∆u+u^σ≤0 on Riemannian manifolds, Comm. Pure Appl. Math., Vol.67(2014), Issue. 8, 1336-1352.(with A.Grigor'yan)