PARTIAL DIFFERENTIAL EQUATION

Course objectives

Knowledge and understanding:The course gives to successful students some advanced tools for the study of various linear and nonlinear PDE's. They will reach a good familiarity with the most recent notions of solutions and their qualitative properties.Skills and attributes:Successful students will able to deal with the advanced study of the solutions to various types of linear and nonlinear PDE's.

Channel 1
LUCA MASSIMO ANDREA MARTINAZZI Lecturers' profile

Program - Frequency - Exams

Course program
First order equations. Transport equation and continuity equation. Conservation laws and Burgers equation. Constant coefficients second order linear equations (Laplace, heat and wave equations)- Second order elliptic equations in divergence form (nonconstant coefficients). L^2 regularity for elliptic equations in divergence form. Second order elliptic equations in non-divergence form. Holder regularity. De Giorgi's theorem and the solution of XIX Hilbert's problem.
Prerequisites
Mathematical analysis, functional analysis, real analysis.
Books
Lecture notes di Clement Mouhot (per il teorema di Cauchy-Kovalevskaya, l'equazioni del trasporto e di Burgers) M. Giaquinta, L. Martinazzi: An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs, second edition, Edizioni della Normale (2012) F. Johns, Partial Differential Equations, Springer
Frequency
Warmly encouraged
Exam mode
Oral exam
Lesson mode
Classroom lectures and homeworks
  • Lesson code1031366
  • Academic year2024/2025
  • CourseMathematics
  • CurriculumAnalisi
  • Year1st year
  • Semester2nd semester
  • SSDMAT/05
  • CFU6
  • Subject areaFormazione teorica avanzata