UBC Math 516, Fall 2017

- Lecture 1 (Sep. 8): the classical linear PDE
- Lecture 2 (Sep. 11): solution of Poisson's equation in R^n
- Lecture 3 (Sep. 13): solution of the heat equation in R^n
- Lecture 4 (Sep. 15): solution of the wave equation in R^n
- Lecture 5 (Sep. 18): properties of harmonic functions: mean value; maximum principle
- Lecture 6 (Sep. 20): properties of harmonic functions: uniqueness; regularity
- Lecture 7 (Sep. 25): properties of the heat equation
- Lecture 8 (Sep. 27): second-order elliptic: weak solutions
- Lecture 9 (Sep. 29): second-order elliptic: Fredholm alternative
- Lecture 10 (Oct. 2): second-order elliptic: interior regularity
- Lecture 11 (Oct. 4): second-order elliptic: boundary regularity
- Lecture 12 (Oct. 6): second-order elliptic: maximum principles
- Lecture 13 (Oct. 13): second-order elliptic: method of sub/super-solutions
- Lecture 14 (Oct. 18): second-order parabolic: weak solutions and energy estimate
- Lecture 15 (Oct. 20): second-order parabolic: existence of weak solutions
- Lecture 16 (Oct. 23): second-order parabolic: regularity of weak solutions
- Lecture 17 (Oct. 25): second-order parabolic: maximum principles
- Lecture 18 (Oct. 27): semigroup theory: semigroups and their generators
- Lecture 19 (Oct. 30): semigroup theory: resolvents
- Lecture 20 (Nov. 1): semigroup theory: Hille-Yosida theorem
- Lecture 21 (Nov. 3): semigroup theory: application to parabolic and hyperbolic problems
- Lecture 22 (Nov. 6): local existence for nonlinear evolution eqns
- Lecture 23 (Nov. 10): local existence in rough spaces
- Lecture 24 (Nov. 20): intro to L^p theory: Calderon-Zygmund inequality
- Lecture 25 (Nov. 27): intro to Di-Giorgi-Nash-Moser theory: Moser iteration
- Lecture 26 (Dec. 1): intro to Schauder theory: Holder estimates; continuity method
- Assignment 1 (due: Fri., Sep. 29); solutions
- Assignment 2 (due: Fri., Nov. 3); solutions
- Assignment 3 (due Wed., Nov. 22); solutions
- Assignment 4 (due Fri., Dec. 1);
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