PILLAR Course: Partial Differential Equations

Monday 3 Nov 2025, 10:45 → Tuesday 10 Feb 2026, 00:15 Europe/Rome

Ex-INPS building (GSSI)

Lecturers
Sara Daneri sara.daneri@gssi.it
Eris Runa eris.runa@gssi.it

Timetable and workload
Lectures: 60 hours
Calendar: available at this link

Course description and outcomes
This course is meant to provide a basic knowledge of and familiarity with the fundamental partial differential equations: elliptic, parabolic and hyperbolic. We will first (and mainly) deal with the linear setting, studying nonlinear extensions in the last part of the course. In the last part we will focus on weak convergence methods and sufficient/necessary conditions for weak lower semicontinuity of energy functionals. The theory will be complemented by interactive exercise sessions. 

Course requirements
Basic functional analysis, Lebesgue spaces.

Course content
Introduction and classification; method of characteristics; harmonic maps and second order linear elliptic equations; second order linear parabolic equations and heat equation; second order linear hyperbolic equations; wave equation; variational approach; weak convergence methods for nonlinear PDEs; weak lower semicontinuity conditions in the calculus of variations and applications.

References
L. C. Evans "Partial Differential Equations"
D. Gilbarg and N. Trudinger "Elliptic partial differential equations of second order"
L.C. Evans "Weak convergence methods for nonlinear partial differential equations"

Examination and grading
Written and oral exam. 

 

Anonymous survey link: here.