The curriculum will be taken from the book
L. C. Evans, Partial differential equations, AMS Graduate Studies in Mathematics, Second edition, 2010,
and the lecture notes.
The lectures will be based on (subject to change)
Chap. 5 (Sobolev spaces)
? 5.1 — H?lder spaces
? 5.2 — Sobolev spaces
? 5.3 — Approximation
? 5.4 — Extensions
? 5.5 — Traces
? 5.6 — Sobolev inequalities
? 5.7 — Compactness
? 5.8 — Additional topics
? 5.9 — Other spaces of functions
Chap. 6 (Elliptic equations)
? 6.1 — Definitions
? 6.2 — Existence of weak solutions
? 6.3 — Regularity
Chap. 7 (Evolution equations)
? 7.1 — Second-order parabolic equations
Appendices