Partial differential equations, fall 2002, J. Hulshof
Credits: 6 ECTS
Examination: homework and oral exam
Hours: Tuesdays 14.45-17.30, Room R2.40 (first session 3-9-2001)
Topics: Hamilton-Jacobi equations and the relation with control problems, Sobolev spaces, weak solutions of linear elliptic and parabolic partial differential equations, maximum principles, regularity theory, techniques for nonlinear equations.
Prerequisites: a general background in analysis and linear algebra, ordinary differential equations, functional analysis.
Literature: Partial Differential Equations, Lawrence C. Evans, American Mathematical Society, Graduate Studies in Mathematics, ISBN: 0-8218-0772-2.
This course is part of the joint master programme for mathematics students at the VU and the UvA. The purpose of the course is to present a broad selection of techniques for several classes of partial differential equations. The course material is largely taken from Evans' recent book on PDE's, which has also been used at the UvA for a more introductionary course in PDE's, see this page. The overlap with and dependence on that course will be minimal. We will also borrow from lecture notes which I collected over the years.
First problem set.
Second problem set.
Third problem set.
Subjects for the oral exam: 5.1-5.7, 6.1, 6.2, 6.4, 6.5, 8.1, 8.2, 8.4, 8.5