Lecturers
Luigi De Rosa luigi.derosa@gssi.it
Eris Runa eris.runa@gssi.it
Timetable and workload
Lectures: 60 hours
Calendar: available at this link
Course content
The course will mainly follow the presentation from the book [Partial Differential Equations - L. C. Evans]. Introduction to PDEs 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; nonlinear PDEs; weak convergence methods; weak lower semicontinuity and applications.
Course requirements
Some good knowledge of calculus and basic functional analysis are required. Theory of Banach spaces; linear bounded operators; dual spaces; weak topology; basic measure theory and Lebesgue integration; L^p spaces; compactness; theory of distributions; weak derivatives; approximation by smooth functions; Fourier transform. Familiarity with Sobolev spaces is highly recommended.
References
L. C. Evans "Partial Differential Equations"
Examination and grading
Written and oral exam.