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, 2.20, 2.21

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