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
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