Equazioni alle Derivate Parziali

C.L. in Matematica e Matematica per le Applicazioni

Universita' di Milano - Anno Accademico 2011/2012

Prof. K. R. Payne


 Programma preliminare del corso (in italiano)    English version

 Programma svolto (incluso riferimenti bibliografici)  (file pdf) (Non ancora disponibile)

 Informazione relative agli esami

 


Avvisi:


Ricevimento studenti:  Mer e Gio 15.30 16.30 e per appuntamento


Materiali didattici:

 

Appunti del corso: (Versione completa del 07/06/2012) PDE Notes (file .pdf con hyperref) Ringraziamenti (file .pdf)

Proposed exercises (in English): (v. i testi dell'anno scorso testi in italiano di molti di loro)

         Chapter 1: Introduction to PDE

Assigned exercises 1.1, 1.2

         Chapter 2: Representation formulas for solutions

Assigned exercises on the transport equation and characteristics: 2.1, 2.2, 2.3

Assigned exercises on Laplaces' equation: 2.5, 2.6, 2.10, 2.13, 2.14, 2.15

Assigned exercises on the heat equation: 2.18, 2.19, 2.20, 2.22, 2.23

Assigned exercises on the wave equation: 2.26, 2.27, 2.30, 2.32

         Chapter 3: Sobolev spaces

Assigned exercises on weak derivatives and elementary examples: 3.1, 3.3, 3.4, 3.5

Assigned exercises on traces: 3.12, 3.13

Assigned exercises Sobolev inequalities and embeddings: 3.16, 3.18, 3.19, 3.27

Assigned exercises on miscellaneous topics: 3.15, 3.22, 3.31

         Chapter 4: Linear elliptic PDE of second order

Assigned exercises on weak solutions to the Dirichlet problem: 4.1, 4.2, 4.5, 4.6

Assigned exercises on the Neumann problem and a fourth order equation: 4.7, 4.9

Assigned exercises the maximum principle and spectral theory: 4.13, 4.14, 4.15, 4.18