Presentations

Schedule

1. Wed, Dec 3: Gradient Estimates for Poisson Equation (Brian Moehring, Yang Zhang)
2. Fri, Dec 5: Interpolation Inequalities (Jacob Shapiro, Qinfeng Li)
3. Mon, Dec 8: Trace Theorem (Yangfan Liu, Ngai Fung Ng)
4. Wed, Dec 10: Oblique Derivative Problem (Andrew Zeller, Daesung Kim)
5. Fri, Dec 12: Lipschitz Functions and $W^{1,\infty}$ (Jian Zhai, Yue Zhao)

Topics

1. Gradient Estimates for Poisson Equation: [GT] Sec 3.4
2. Interpolation Inequalities: [GT] Sec 6.8
3. Trace Theorem: [A] 5.20-5.22 (and 6.1-6.8); see also [E] Sec 5.5
4. Oblique Derivative Problem: [GT] Sec 6.7 (Poisson Equation only)
5. Lipschitz Functions and $W^{1,\infty}$: [E] 5.8.2-5.8.3

References
[A] R. Adams, Sobolev Spaces
[GT] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed.
[E] L.C. Evans, Partial Differential Equations, 2nd ed.

Course Log

Here you will find information about the material that was already covered or will be covered in the next few lectures.

Covered

• Mon, Dec 1:  §8.5 (finish) 
• Nov 24-28: No class (Thanksgiving Break)
• Fri, Nov 21: §8.5
• Wed, Nov 19:  De Giorgi's method: Oscillation Lemma
• Mon, Nov 17: De Giorgi's method: $L^\infty$-$L^2$ estimate
• Fri, Nov 14: §8.4 
• Wed, Nov 12: §8.3
• Mon, Nov 10: §8.2
• Fri, Nov 7: Chap 8, §8.1
• Wed, Nov 5: §7.10, §7.12, §6.9
• Mon, Nov 3: §7.9
• Fri, Oct 31: §7.8 (finish)
• Wed, Oct 29: §7.7 (finish), §7.8 (start)
• Mon, Oct 27: §7.7
• Fri, Oct 24: §7.5, §7.6, §7.7(start)
• Wed, Oct 22: §7.3, §7.4
• Mon, Oct 20: §7.1, §7.2
• Fri, Oct 17: §6.4 (finish), §7.1(start)
• Wed, Oct 15:§6.4
• Mon, Oct 13: October Break
• Fri, Oct 10: §6.3 (finish)
• Wed, Oct 8: §6.2 (finish), §6.3 (start), §5.2
• Mon, Oct 6: §6.2
• Fri, Oct 3: §6.1 (finish)
• Wed, Oct 1: Started Chap 6 and §6.1
• Mon, Sep 29: §4.5
• Fri, Sep 26: §4.4
• Wed, Sep 24: §4.3 (cont)
• Mon, Sep 22: §4.3 
• Fri, Sep 19:  §4.2
• Wed, Sep 17:  §3.3 (finish),  §4.1
• Mon, Sep 15: §3.2 (finish), §3.3
• Fri, Sep 12: §3.1 (finish), §3.2 (start)
• Wed, Sep 10: § 2.8 (finish), §2.9, started Chap 3, §3.1
• Mon, Sep 8: §2.8 (cont)
• Fri, Sep 5: §2.7 (finish), §2.8
• Wed, Sep 3:  §2.6 (finish), §2.7
• Mon, Sep 1: No Class (Labor Day)
• Fri, Aug 29: §2.4 (cont), §2.5, §2.6
• Wed, Aug 27: §2.2 (cont), §2.3, §2.4
• Mon, Aug 25: §2.1, §2.2 (start)

Homework

Homework assignments will generally be from [GT].

4. Due Mon, Oct 20: [GT] 6.1, 6.2  
3. Due Fri, Oct 3: [GT] 4.3, 4.8
2. Due Mon, Sep 22: [GT] 2.12, 3.2 (a,b)
1. Due Mon, Sep 8: [GT] 2.3, 2.13

Announcements

Welcome to MA64200 course webpage!

Course Information

Time and Place: MWF 10:30am–11:20pm in UNIV 119

Instructor: Arshak Petrosyan

Office Hours: MWF 9:30-10:30, or by appointment, in MATH 610

Textbook: [GT] Gilbarg, Trudinger, Elliptic partial differential equations of second order, 2nd edition; Springer-Verlag, Berlin

Description: This is the first semester in a one-year course on the theory of PDEs. The Fall semester focuses on linear second order elliptic equations. Topics to be covered include Laplace's equation, the maximum principle, Poisson's equation and the Newtonian potential, Schauder's estimates for classical solutions, Sobolev Spaces, weak solutions and their regularity.