Equazioni alle Derivate Parziali
Corso di Laurea in Matematica
Università di Milano - Anno Accademico 2015/2016
Prof. K. R. Payne
Programma
preliminare del corso
Preliminary syllabus of the course
Avvisi/Announcements:
·
Prossimi Appelli NEW!!!
o 23 gennaio (data ufficiale
dell’appello)
n Date effettive dell’appello: VEN
20 gennaio e LUN 30 gennaio
n E’ necessario comunicare la
scelta della data entro 2 giorni prima della data effettiva voluta
o 13 febbraio (data ufficiale
dell’appello) con data effettiva da concordare con il docente
·
Per
fare l’esame si deve iscriversi sul sito SIFA (In order to take
the final oral exam, it is necessary to be registered using the SIFA site)
·
Esercizi proposti per tutto il corso sono
disponibile sotto (Proposed exercises
for the entire course are available below)
Ricevimento/Office Hours: MER e GIO 14.30 – 15.30 e per appuntamento (WED and THUR 14.30-15.30 and by appointment)
Materiali
Didattici/Teaching Materials:
Appunti del Corso/Class Notes
(in Italian): (Versione di 11 marzo, 2016) PDE Notes (file .pdf con hyperref)
Ringraziamenti (file .pdf) Anche grazie
a Davide Piazzoli (studente dell’ a.a.
2011-2012) e Arianna Casanova Flores (studente dell’a.a. 2013-2014) per le loro correzioni!
Proposed exercises (in English):
1. Chapter 1: Introduction to PDE
Assigned exercises: 1.1,
1.2
2. Chapter 2: Representation
formulas for solutions
Assigned exercises on the
transport equation 2.1, 2.2, 2.3
Assigned exercises on Laplaces'
equation: 2.5, 2.6, 2.8, 2.9, 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18,
2.19
3.
Chapter 3: Sobolev spaces (Corrected Version of 10
June, 2016 – Thanks to Laura Mauri for the input!)
Assigned exercises on weak
derivatives and elementary examples: 3.1, 3.3, 3.4, 3.5, 3.6, 3.7
Assigned exercises on Sobolev spaces and basic properties: 3.7, 3.9, 3.10, 3.11,
3.12, 3.13,
Assigned exercises traces
and embeddings: 3.14, 3.15, 3.18, 3.19, 3.21, 3,22,
3.23, 3.24, 3.28, 3.29, 3.30, 3.31, 3.32, 3.33
4.
Chapter 4: Elliptic PDE
of second order
Assigned exercises on
elliptic operators and existence theory: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7,
4.8, 4.9, 4.10, 4.11, 4.12
Assigned exercises on
regularity and the maximum principle: 4.13, 4.14, 4.15, 4.17, 4.18, 4.23
Assigned exercises on
eigenvalues and eigenfunctions: 4.19, 4.20, 4.21,
4.22
Problem Session 1: We will discuss exercises
1.1, 1.2, 2.1, 2.2, 2.3, 2.5, 2.6, 2.8, 2.9, 2.11, 2.20, 2.21
Problem Session 2: We will discuss exercises
3.1, 3.2, 3.3, 3.6, 3.9, 3.10, 3.12, 3.19, 3.23, 3.24
Problem Session 3: We will discuss exercises
3.28, 3.30, 4.1, 4.3, 4.4, 4.5, 4.11, 4.12
Problem Session 4: We will discuss exercises
4.19, 4.23, 4.18