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

·         Chapter 3: Sobolev spaces

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