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Instructor: Stephen Gustafson, Math
115, phone 604-822-3138,
gustaf@math.ubc.ca
Office Hours:
by appointment
Course
outline
Lectures:
Mon/Wed/Fri 1:00 - 1:50 in MATX 1118
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Lecture 1 (Sep. 8): the classical linear PDE
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Lecture 2 (Sep. 11):
solution of Poisson's equation in R^n
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Lecture 3 (Sep. 13):
solution of the heat equation in R^n
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Lecture 4 (Sep. 15):
solution of the wave equation in R^n
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Lecture 5 (Sep. 18):
properties of harmonic functions: mean value; maximum principle
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Lecture 6 (Sep. 20):
properties of harmonic functions: uniqueness; regularity
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Lecture 7 (Sep. 25):
properties of the heat equation
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Lecture 8 (Sep. 27):
second-order elliptic: weak solutions
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Lecture 9 (Sep. 29):
second-order elliptic: Fredholm alternative
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Lecture 10 (Oct. 2):
second-order elliptic: interior regularity
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Lecture 11 (Oct. 4):
second-order elliptic: boundary regularity
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Lecture 12 (Oct. 6):
second-order elliptic: maximum principles
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Lecture 13 (Oct. 13):
second-order elliptic: method of sub/super-solutions
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Lecture 14 (Oct. 18):
second-order parabolic: weak solutions and energy estimate
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Lecture 15 (Oct. 20):
second-order parabolic: existence of weak solutions
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Lecture 16 (Oct. 23):
second-order parabolic: regularity of weak solutions
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Lecture 17 (Oct. 25):
second-order parabolic: maximum principles
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Lecture 18
(Oct. 27):
semigroup theory: semigroups and their generators
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Lecture 19
(Oct. 30):
semigroup theory: resolvents
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Lecture 20
(Nov. 1):
semigroup theory: Hille-Yosida theorem
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Lecture 21
(Nov. 3):
semigroup theory: application to parabolic
and hyperbolic problems
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Lecture 22
(Nov. 6):
local existence for nonlinear evolution eqns
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Lecture 23
(Nov. 10):
local existence in rough spaces
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Lecture 24
(Nov. 20):
intro to L^p theory: Calderon-Zygmund inequality
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Lecture 25
(Nov. 27):
intro to Di-Giorgi-Nash-Moser theory: Moser iteration
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Lecture 26
(Dec. 1):
intro to Schauder theory: Holder estimates; continuity method
Homework Assignments:
Reference
list
Back to S. Gustafson's homepage
or UBC Math.
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