MENU

You are here

Introduction to Elliptic Equations

Lecturer: 
Course Type: 
PhD Course
Master Course
Anno (LM): 
Second Year
Academic Year: 
2021-2022
Period: 
October-January
Duration: 
50 h
Description: 

1. Laplace equation:

  • harmonic functions, mean value properties,
  • maximum principle,
  • Green's function,
  • Poisson kernel,
  • Harnack inequality,
  • subharmonic functions,
  • Perron-Wiener-Brelot method for the Dirichlet problem,
  • regular boundary points.

2. Variational theory of elliptic equations:

  • existence and uniqueness of weak solutions in Sobolev Spaces,
  • weak maximum principle,
  • eigenvalues and eigenfunctions,
  • regularity theory in Sobolev spaces and in spaces of Hölder continuous functions.

3. Some remarks on nonlinear elliptic equations:

  • Euler equations for minimum problems of the calculus of variations,
  • direct methods for the existence of a minimum point,
  • monotonicity methods for existence and uniqueness of solutions to some nonlinear problems,
  • variational inequalities,
  • use of fixed points theorems for the solution of some nonlinear partial differential equations.
Location: 
A-134
Next Lectures: 
Thursday, October 21, 2021 - 16:30 to 18:30
Wednesday, October 27, 2021 - 16:30 to 18:30
Thursday, October 28, 2021 - 16:30 to 18:30
Wednesday, November 3, 2021 - 16:30 to 18:30
Thursday, November 4, 2021 - 16:30 to 18:30
Wednesday, November 10, 2021 - 16:30 to 18:30
Thursday, November 11, 2021 - 16:30 to 18:30
Wednesday, November 17, 2021 - 16:30 to 18:30
Thursday, November 18, 2021 - 16:30 to 18:30
Wednesday, November 24, 2021 - 16:30 to 18:30
Thursday, November 25, 2021 - 16:30 to 18:30
Wednesday, December 1, 2021 - 16:30 to 18:30
Thursday, December 2, 2021 - 16:30 to 18:30
Wednesday, December 8, 2021 - 16:30 to 18:30
Thursday, December 9, 2021 - 16:30 to 18:30
Wednesday, December 15, 2021 - 16:30 to 18:30
Thursday, December 16, 2021 - 16:30 to 18:30
Wednesday, December 22, 2021 - 16:30 to 18:30
Thursday, December 23, 2021 - 16:30 to 18:30
Wednesday, January 12, 2022 - 16:30 to 18:30

Sign in