Personal Web Page of Sagun Chanillo

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Recent Publications

• Isoperimetric Inequalities and Volume Comparison theorems on CR manifolds(with Paul Yang)
• Regularity of the Minimizers in the Composite Membrane Problem in R^2(with Carlos Kenig and Tung To)
• Subelliptic Bourgain-Brezis estimates on Groups (with Jean Van Schaftingen)
• Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds( with J.J. Manfredi)
• Weak Uniqueness and Partial Regularity for the Composite Membrane Problem(with C. Kenig)
• Schrodinger Equations on Complex Semi-simple Lie Groups
• Plateau Problem-H Surface Eqn.(A. Malchiodi)
• Non-Linear Eigenvalues and Analytic Hypoellipticity (B. Helffer, A. Laptev)
• Composite Membranes and Symmetry Breaking (D. Grieser, K. Kurata, M. Imai, I. Ohnishi)
• The Free Boundary Problem for Composite Membranes, Contemporary Math. of the AMS v. 268, (2000)(D. Grieser, K. Kurata)
• The Conformal Plate Buckling Eqn.(M. Kiessling)
• The Difference of Topology in Changing Sign Yamabe Problems, the case of two masses on S^3 (A. Bahri)

Some Older Publications

• Surfaces with Prescribed Gauss Curvature( A statistical Mechanics approach)( with M. Kiessling)
• Level lines of solutions to Non-Linear PDE in two dimensions (X. Cabre)
• First eigenvalue of the Hodge Laplacian (F. Treves)
• Local Exactness in Differential Complexes (Francois Treves)
• Borg-Levinson Theorem and Inverse Problems for the Dirichlet to Neumann Map.
• Liouville's Eqn. and Conformally Invariant Systems of PDE of Liouville type, Toda Lattices (M. Kiessling)
• Continuity of solutions to Divergence form Elliptic eqns. in R^2 and Compensated Compactness (Yanyan Li)
• On Diameters of Uniformly Rotating white dwarf stars( with Yanyan Li)
• Symmetry and Symmetry Breaking of Solutions to Non-Linear PDE in Physics and Geometry(M. Kiessling)

Research Monograph on Jacobi Polynomials

Optimal Weak type Inequalities for the Partial Cesaro Sum operator for Jacobi Polynomials

Course Information(Introduction to PDE, Math 423 Fall 2009)

Here is a basic handout for the course with the grading policy, and other pertinent course information.

A lecturewise syllabus for the course is contained in this handout

This is an UPDATED list of homework problems upto Chap 5 for Math 423

Here are a set of notes on the wave equation.

Here is a set of notes on the Riemann problem for Shocks and Hugoniot Curves.

Some notes on the characteristic method.

Musical instruments are tied to the wave eqn. In particular note how the different types of boundary conditions affects the tone. Read this article on musical instruments carefully as Homework.

Here is a review sheet for the course.

Homework due on 11/19: Sec 5.1, 2,5,9; sec 5.2, 11; sec 5.4, 6, 7(a), (b), (c), 12,

MID-TERM EXAM 2 on 11/19. Covers Sec 2.3(Maximum Principle), secs 4.1-4.3, 5.1, 5.2, 5.4.

FINAL EXAM: Thursday 12/17, 8-11pm

Solutions to quiz 2.

Solutions to test 1.

TEST 1 GRADING CURVE: 0-40F, 41-50D, 51-64C, 65-70C+, 71-79B, 80-88B+, 89-100 A, Highest score:98.

You can download a free version of SCILAB from the Scilab Homepage

Some Interesting Articles related to Mathematics

Maintained by chanillo@math.rutgers.edu and last modified 10/15/2009