完全非线性偏微分方程短期课程

主讲人:王志张教授(复旦大学)

课程简介:

In this course, we would like to mention some topics of the k-Hessian equations. We first give a preliminary, then we will talk about the Dirichlet problem, the global curvature estimates and the applicaiton of these estimates in Minkowski space.

Time:  

  1.  14:00-15:30, Dec 18

  2.  10:30-12:00, Dec 22

  3.  14:00-15:30, Dec 25

  4.  10:30-12:00, Dec 29

Venue:  数学中心研讨室(至善楼602)

Online:  Zoom:811 5638 1768(Password:msrc)

Reference:

[1] Caffarelli, L.A., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian. Acta Math. 155, 261–301 (1985).

[2] Lin,M.,Trudinger,N.S.:Onsomeinequalitiesforelementarysymmetricfunctions.Bull.Austral.Math. Soc. 50, 317–326 (1994).

[3] N.S. Trudinger, On the Dirichlet problem for Hessian equations, Acta Math. 175 (1995) 151–164.

[4] Li,M.,Ren,C.,Wang,Z.:Aninteriorestimateforconvexsolutionsandarigiditytheorem.J.Funct.Anal. 270, 2691–2714 (2016).

[5] Zhizhang Wang, Ling Xiao, Entire spacelike hypersurfaces with constant σk curvature in Minkowski space, Math. Ann. 382 (3–4) (2022) 1279–1322.