**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**