Equazioni alle Derivate Parziali
C.L. in
Matematica e Matematica per le Applicazioni
Universita' di Milano - Anno
Accademico 2013/2014
Prof. K. R. Payne
Programma
preliminare del corso (in italiano)
English version
Information about the final exam
Announcements:
· One must be registered (SIFA) in order to take the final exam
· Updated version of the class notes available below
· Exercises (version of 17 march) available below
Office Hours: Thursday 14.30 – 16.30 and by appointment
Teaching Materials:
Course Notes: (Version of March 13) PDE Notes (file .pdf con hyperref)
Ringraziamenti (file .pdf) Anche grazie
a Davide Piazzoli (studente dell’ a.a.
2011-2012) per le sue correzioni!
Proposed exercises (in English):
·
Chapter
1: Introduction to PDE
Assigned exercises: 1.1, 1.2
· Chapter 2: Representation formulas for solutions
Assigned exercises on Laplaces' equation: 2.5, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, 2.19, 2.20, 2.21
Assigned exercises on weak derivatives and
elementary examples: 3.1, 3.2, 3.3, 3.4, 3.5
Assigned exercises on traces: 3.11, 3.12,
3.18, 3.19
Assigned exercises Sobolev
inequalities and embeddings: 3.14, 3.16, 3.17, 3.26
Assigned exercises on miscellaneous topics: 3.30
· Chapter 4: Linear elliptic PDE of second order
Assigned exercises on weak solutions to the Dirichlet problem: 4.1, 4.2, 4.6, 4.7, 4.8
Assigned exercises on the Neumann problem,
other boundary conditions and a fourth order equation: 4.9, 4.10, 4.11
Assigned exercises the maximum principle and
spectral theory: 4.15, 4.16, 4.17, 4.18, 4.19, 4.20