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 Valutazione

Resolution of home exercises proposed by the teacher.

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 Valutazione

Resolution of home exercises proposed by the teacher.