20410758 - AM410 - MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS

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

teacher profile | teaching materials

Fruizione: 20410757_1 AM410- MODULO A - INTRODUZIONE ALLE EQUAZIONI ALLE DERIVATE PARZIALI in Matematica LM-40 ESPOSITO PIERPAOLO

Programme

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.

Core Documentation

“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

Type of delivery of the course

The course plans lectures. Attendance is not required but strongly suggested.

Type of evaluation

Resolution of home exercises proposed by the teacher.

teacher profile | teaching materials

Fruizione: 20410757_1 AM410- MODULO A - INTRODUZIONE ALLE EQUAZIONI ALLE DERIVATE PARZIALI in Matematica LM-40 ESPOSITO PIERPAOLO

Programme

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.

Core Documentation

“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

Type of delivery of the course

The course plans lectures. Attendance is not required but strongly suggested.

Type of evaluation

Resolution of home exercises proposed by the teacher.