MA 676, Analysis I
- Course Syllabus, pdf file
- Homework One : Chapter 1: 1(j)(r)(s); 2, 14, 15, 17.
- Homework Two : Chapter 2: 1, 4, 5, 6; 7, 9, 10, 16.
- Homework Three : Chapter 3: 9, 10, 12, 20.
pdf file
- Review Problem for Midterm :
pdf file
- Midterm Exam Problem : pdf file
- Solution to Midterm : pdf
file
- Homework Four : Chapter 4: 4, 5, 15, 16, 17, 18.
- Homework Five : pdf file;
pdf file.
PDE Seminar, Spring 2008
(Time:11-12:00pm Tuesday; Room: CB 243)
Previous analysis/pde seminar
Previous Publications (Partially supported by NSF grants):
Recent Publications (The research
reported in the following papers is supported by NSF grants
DMS 0400718 and DMS 0601162)
- 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
(with Y. Yu), in press. dvi file .
- Derivation of the Aronsson equation for C-1 Hamiltonians.
Trans. AMS (with M. Crandall, Y. Yu), in press. pdf file .
- Uniqueness and nonuniqueness of viscosity solutions to Aronsson's
equation. Arch. Ration Mech. Anal. (with
R. Jensen, Y. Yu), in press. pdf file .
- Aronsson's equation on Carnot-Carath\'eodory spaces.
To appear, Illinois Journal of Mathematics (with Y. Yu). pdf
file .
Preprints
- Landau-Lifshitz-Maxwell equation in dimension three.
Preprint, 2008 (with S.J. Ding, X.G. Liu).
pdf file .
- Boundary regularity for polyharmonic maps in the critical dimension.
Preprint, (2008) (with T. Lamm). pdf file .
Monograph
- The Analysis of Harmonic Maps and Their Heat Flows, 280 pages
(with F. H. Lin). World Scientific Publisher Inc (in press).
(Due to the obligation for contract, the pdf file of the
monograph, which is scheduled to be in print by June 2008, will not be uploaded here).
