Welcome to Changyou Wang's homepage

• MA 114, Calculus II
• MA 633, Partial Differential Equations II

Fall 2010

• MA 113, Calculus I
• MA 533, Partial Differential Equation

Fall 2009-Spring 2010

• On scholarly leave: visit IMA from September 2009 to June 2010

Spring 2009

• MA214, Calculus IV
• MA 773, Introduction to Geometric Measure Theory

Spring 2007

• MA214, Calculus IV
• MA641G, Differential Geometry

Fall 2007

• MA213, Calculus III
• MA575, Principle of Mathematical Analysis

Spring 2008

• MA114, Calculus II
• MA 676, Analysis I

Fall 2008

• MA 213, Calculus III
• MA 677, Analysis II

Previous analysis/pde seminar

• Spring 2009
• Fall 2008
• Spring 2008
• Fall 2007
• Spring 2007
• Fall 2006

Previous Publications(Partially supported by NSF grants):

• Click here to access the list of publications

Recent Publications

• Stable stationary harmonic maps into spheres. Acta Math. Sinica (Engl. Ser.) 22 (2006), no. 2, 319-330 (with FangHua Lin). pdf file.
• On Landau-Lifshitz equation in dimensions at most four. Indiana Univ. Math. J. Vol. 55, no.6 (2006) 1615-1644. dvi file.
• Generalized cone comparison principle for viscosity solutions of the Aronsson equation and absolute minimizers. Comm. P.D.E. V. 31, No. 7 (2006) 1027-1046 (with R. Gariepy, Y. Yu). dvi file .
• The Aronsson equation for absolute minimizers of $L^\infty$ functionals associated with vector fields satisfying H\"ormander's conditions. Trans. AMS. 359 (2007), 91-113. dvi file.
• Heat flow of biharmonic maps in dimension four and its application. Pure and Applied Math. Quarterly, Vol. 3, No. 2 (2007) 595-613 (Special issue: In honor of L. Simon, Part 1 of 2). pdf file.
• Finite time singularity of the Landau-Lifshitz-Gilbert equation. Int. Math. Reas. Notices, Vol. 2007 (with Shijin Ding). pdf file
• Asymptotic behavior of infinity harmonic functions near an isolated singularity. Int. Math. Reas. Notices, Vol. 2008, article ID rnm163, 23 pages (with O. Savin, Y. Yu). pdf file .
• Heat flow of harmonic maps whose gradients belong to $L^n_xL^\infty_t$. Arch. Rational Mech. Anal. 188 (2008), 309-349. pdf file
• Harmonic maps from manifolds of $L^\infty$-Riemannian metrics. Calc. Var. & PDE (2008), Vol 32, 387-405 (with W. Ishizuka). pdf file .
• $C^1$-regularity of the Aronsson equation in $\R^2$, Annales I'Institut H. Poincar\'e- Analyse non lin\'eaire, 25 (2008) 659-678 (with Y. Yu). dvi file .
• Uniqueness and nonuniqueness of viscosity solutions to Aronsson's equation. Arch. Ration Mech. Anal. (with R. Jensen, Y. Yu), Vol. 190, no. 2 (2008) 347-370. pdf file .
• Derivation of the Aronsson equation for C-1 Hamiltonians. Trans. AMS 361 (2009) 103-124(with M. Crandall, Y. Yu). pdf file .
• Aronsson's equation on Carnot-Carath\'eodory spaces. Illinois Journal of Mathematics, Vol. 52, No. 3, Fall 2008, 757-772 (with Y. Yu). pdf file .
• Boundary regularity for polyharmonic maps in the critical dimension. Advances in Calculus of Variations 2, 2009, No. 1, 1-16(with T. Lamm). pdf file .
• Regularity of Dirac-harmonic maps. Int. Math. Reas. Notices, 2009, no. 20, 3759-3792 (with D. L. Xu). pdf file .
• Landau-Lifshitz-Maxwell equation in dimension three. Pacific J. Math., Vol. 243, No. 2, 2009, 243-276(with S.J. Ding, X.G. Liu). pdf file .
• Liquid crystall flows in two dimensions. Arch. Ration. Mech. Anal., 197 (2010) 297-336 (with F. H. Lin, J. Y. Lin) pdf file .
• Notes on the regularity of harmonic map systems. Proceedings of American Mathematical Society, 138 (2010) no. 6, 2015-2023 (with T. Huang) pdf file .
• A Remark on Nonlinear Dirac Equations. Proceedings of American Mathematical Society, 138 (2010), 3753-3758. pdf file .
• Weak solution to compressible hydrodynamic flow of liquid crystals in 1D. DCDS-B,15 (2011), no. 2, 357–371(with S. J. Ding, Y. H. Wen). pdf file .
• Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data. Arch. Ration. Mech. Anal., 200 (2011), no. 1, 1–19. pdf file .
• On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals. Chinese Annals of Mathematics, Ser. B 31 (2010), no. 6, 921–938(with F. H. Lin). pdf file .
• Well-posedness for the heat flow of polyharmonic maps with rough initial data. Advances in Calculus of Variations, 4 (2011), no. 2, 175–193. (with T. Huang). pdf file .
• On the heat flow of equation of surfaces of constant mean curvature. Manuscripta Math., 134 (2011), no. 1-2, 259–271 (with T. Huang, Z. Tan). pdf file .
• Well-posedness for the heat flow of biharmonic maps with rough initial data. J. Geom. Anal., 22 (2012), no. 1, 223–243. pdf file .
• Compressible hydrodynamic flow of liquid crystals in 1D. DCDS-A, 32 (2012), no. 2, 539–563(with S. J. Ding, J. Y. Lin, Y. H. Wen). pdf file .
• Phase transitions for potentials of high dimensional wells. CPAM, 65 (2012), no. 6, 833–888 (with F. Lin, and X. Pan). pdf file .
• Strong solutions of the compressible nematic liquid crystal flow. JDE, 252 (2012), no. 3, 2222–2265 (with T. Huang, H. Y. Wen). pdf file .
• Boundary regularity of stationary biharmonic maps. CVPDE, 45 (2012), no. 1-2, 165–191 (with Huajun Gong, Tobias Lamm). pdf file .
• Blow up criterion for compressible nematic liquid crystal flows in dimension three. ARMA, 204 (2012), no. 1, 285–311(with T. Huang, H. Y. Wen). pdf file .
• Blow up criterion for nematic liquid crystal flows, CPDE, 37 (2012), no. 5, 875–884 (with T. Huang). pdf file .
• Energy identity for a class of approximate biharmonic maps into sphere in dimension four, DCDS-A, 33 (2013), no. 2, 861–878 (with Shenzhou Zheng).arXiv:1110.6536 pdf file .
• Energy identity for approximate biharmonic maps to Riemannian manifolds and its application, Journal of Functional Analysis, 263 (2012), no. 4, 960–987 (with Shenzhou Zheng). arXiv:1112.6362 pdf file .
• $C^1$-boundary regularity of planar infinity harmonic functions, Math. Res. Lett., 19 (2012), no. 4, 823–835(with Yifeng Yu). pdf file .
• Well-posedness of nematic liquid crystal flow in $L^3_uloc(R^3)$, Arch. Ration. Mech. Anal, to appear (with J. Hineman) pdf file .
• Harmonic maps on domains with piecewise Lipschitz continuous metrics. Pacific J. Math., to appear (with Haigang Li). pdf file .

Preprints

• On uniqueness of heat flow of harmonic maps (with T. Huang). pdf file .
• Regularity and uniqueness of the heat flow of biharmonic maps (with J. Hineman, T. Huang). pdf file .
• Partial regularity of suitable weak solutions to the liquid crystal flow in three dimensions. In preparation (with F. H. Lin).
• Boundary regularity for a new class of minimizing harmonic maps. In preparation (with F. H. Lin).

Monography

• The Analysis of Harmonic Maps and Their Heat Flows, 267 pages (with F. H. Lin), by World Scientific Publisher Inc, ISBN-109812779523.
  
• An Introduction of Infinity Harmonic Functions. Preprint, 2008. pdf file .
• An open question on regularity of Aronsson's equation. Communications in Mathematical Analysis, Proceeding of the 2006 Midwest Geometry Conference, pp. 80-83 (2008), edited by E. B. Lin, W. Wei. pdf file