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.