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Faculty

Yue He Associate Professor

Research Interests: 
  • Partial Differential Equations
  • Geometric analysis
  • Symplectic Geometry and Mathematical Physics
Bio: 

Educational Background

  • PhD, Degenerate elliptic and parabolic PDEs, Fudan University (2003)
  • MA, Evolution equation and Infinite dimensional dynamical systems, Yunnan University (1995)
  • BA, mathematics, Yunnan University, (1992)

 

Research

Research Interests

(1)Partial Differential Equations: 

nonlinear elliptic and parabolic PDEs, degenerate elliptic and parabolic PDEs,  mixed type PDEs, concavity and convexity of free boundary.

(2)Geometric analysis: 

(estimates and nodel set) of (Laplacian and Steklov) eigenvalue,

minimal surface (Willmore conjecture and the related problems), mean curvature flows, Ricci flows, gradient estimate, Li-Yau-Hamilton inequality.

(3) Symplectic Geometry and Mathematical Physics

Journal Articles

Publications:

  1. Yue He, Well-posedness and regularity of boundary value problems for a class of second-order degenerate semilinear elliptic equations,(Chinese) Chinese Ann. Math. Ser. A, 25 (2004), no. 2, 225–242. 
  2. Yue He, Higher-order regularity of solutions to the Dirichlet problem for a class of degenerate elliptic equations,(Chinese) J. Nanjing Norm. Univ. Nat. Sci. Ed., 30 (2007), no. 1, 28–32.
  3. Yue He, Well-posedness of boundary value problems for a class of degenerate elliptic equations, (Chinese) Chinese Ann. Math. Ser. A, 28 (2007), no. 5, 651--666; translation in Chinese J. Contemp. Math.,  28 (2007), no. 4, 393–410
  4. Hairong Yuan and Yue He, Transonic potential flows in a convergent-divergent approximate nozzle, J. Math. Anal. Appl. , 353 (2009), no. 2, 614–626. 
  5. Yue He, On sharp lower bound of the gap for the first two eigenvalues in the Schrödinger operator, Taiwanese J. Math. , 17 (2013), no. 1, 1–13.
  6. Yue He, A lower bound for the first eigenvalue in the Laplacian operator on compact Riemannian manifolds, Journal of Geometry and Physics, 71 (2013) 73–84. 
  7. Yue He,Sharp lower bound of the spectral gap for a Schrödinger operator and related results, Front. Math. China, 10 (2015), no. 6, 1283–1312. 
  8. Yue He,  New estimates of lower bound for the first eigenvalueon compact manifolds with positive richll,hx bouss 
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