Yuhua Sun

2004.09-2008.07 Jilin University (Bachelor)

2008.09-2013.01 Tsinghua University (Docotor)

2011.09-2014.07  Bielefeld University (Doctor)

2016.12-now Associate Professor (Nankai University)

2014.10-2016.12 Lecturer (Nankai University)

Analysis on Manifolds and PDEs

Partial Differential Equation, Calculus, Linear Algebra, Ordinary Differential Equation

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)

If you are interested in my research, you could contact me by my email:sunyuhua@nankai.edu.cn; If you would like to visit me, our local Chern insitute could provide local support for visitor. For more details please visit

http://222.30.49.69/nim_e/visitor.htm

Selected Papers:

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)