The curriculum will be taken from the book
L. C. Evans, Partial differential equations, AMS Graduate Studies in Mathematics, Second edition, 2010.
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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
- 6.4 — Maximum principles
- 6.5 — Eigenvalues and eigenfunctions
Chap. 7 (Evolution equations)
- 7.1 — Second-order parabolic equations
- 7.4 — Semigroup theory
Appendices