72725 - Partial Differential Equations

Course Unit Page

Academic Year 2017/2018

Learning outcomes

At the end of the course the student knows  basic notions from the theory od Elliptic, Parabolic and Hyperbolic Partial Differentia Equations. He is able to study and understand   elementary
differential models  in applied sciences. He is also able to face high level topics from the general
theory of Partial Dirrential Equations.

Course contents

Linear second order partial differential operators with non-negative characteristic form: Picone's maximum principle, strong maximum principle, maxima propagation.

Potential theory and Dirichlet problem in abstract harmonic spaces.

Applications to elliptic-parabolic PDE's arising in theoretical and applied settings: sub-Laplacians and related heat operators on stratified Lie groups, Kolmogorov-Fokker-Planck operators.

Readings/Bibliography

After notes of the lectures.

Teaching methods

The course consists of lessons describing the fundamental concepts of the program. Lessons are completed with examples illuminating the theoretical content. Futhermore exercises are solved in the classroom.

Assessment methods

1) Homework: solution of some problems form a list given by the lecturer.
2) Oral exams on some arguments, chosen by the student, from the main
chapters of the course.

Office hours

See the website of Ermanno Lanconelli

See the website of Giovanni Cupini