To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
Curriculum
scheda docente
materiale didattico
"Partial differential equations. Second edition", Lawrence C. Evans, Graduate Studies in Mathematics 19, American Mathematical Society
Fruizione: 20410757_1 AM410- MODULO A - INTRODUZIONE ALLE EQUAZIONI ALLE DERIVATE PARZIALI in Matematica LM-40 ESPOSITO PIERPAOLO
Programma
Preliminaries: definition of hyper-surface, integration on hyper-surfaces, the divergence theorem; the Laplace equation: the mean value inequalities, the minimum and maximum principle, the Harnack inequality, the Green representation, the Poisson integral, convergence's theorems, interior estimates on the derivatives, the Perron method for the Dirichlet problem.Testi Adottati
“Elliptic partial differential equations of second order. Reprint of the 1998 edition”, D. Gilbarg e N.S. Trudinger, Classics in Mathematics, Springer-Verlag"Partial differential equations. Second edition", Lawrence C. Evans, Graduate Studies in Mathematics 19, American Mathematical Society
Modalità Erogazione
The course plans lectures. Attendance is not required but strongly suggested.Modalità Valutazione
Resolution of home exercises proposed by the teacher.
scheda docente
materiale didattico
"Partial differential equations. Second edition", Lawrence C. Evans, Graduate Studies in Mathematics 19, American Mathematical Society
Fruizione: 20410757_1 AM410- MODULO A - INTRODUZIONE ALLE EQUAZIONI ALLE DERIVATE PARZIALI in Matematica LM-40 ESPOSITO PIERPAOLO
Programma
Preliminaries: definition of hyper-surface, integration on hyper-surfaces, the divergence theorem; the Laplace equation: the mean value inequalities, the minimum and maximum principle, the Harnack inequality, the Green representation, the Poisson integral, convergence's theorems, interior estimates on the derivatives, the Perron method for the Dirichlet problem.Testi Adottati
“Elliptic partial differential equations of second order. Reprint of the 1998 edition”, D. Gilbarg e N.S. Trudinger, Classics in Mathematics, Springer-Verlag"Partial differential equations. Second edition", Lawrence C. Evans, Graduate Studies in Mathematics 19, American Mathematical Society
Modalità Erogazione
The course plans lectures. Attendance is not required but strongly suggested.Modalità Valutazione
Resolution of home exercises proposed by the teacher.