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Introduction to Elliptic Equations

Lecturer: 
Gianni Dal Maso
Course Type: 
PhD Course
Master Course
Anno (LM): 
Second Year
Academic Year: 
2017-2018
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-133
Next Lectures: 
Thursday, October 26, 2017 - 09:00 to 11:00
Friday, October 27, 2017 - 09:00 to 11:00
Thursday, November 9, 2017 - 09:00 to 11:00
Friday, November 10, 2017 - 09:00 to 11:00
Thursday, November 16, 2017 - 09:00 to 11:00
Friday, November 17, 2017 - 09:00 to 11:00
Thursday, November 23, 2017 - 16:00 to 18:00
Friday, November 24, 2017 - 09:00 to 11:00
Thursday, November 30, 2017 - 09:00 to 11:00
Friday, December 1, 2017 - 09:00 to 11:00
Thursday, December 7, 2017 - 09:00 to 11:00
Thursday, December 14, 2017 - 09:00 to 11:00
Friday, December 15, 2017 - 09:00 to 11:00
Thursday, December 21, 2017 - 09:00 to 11:00
Friday, December 22, 2017 - 09:00 to 11:00
Thursday, January 11, 2018 - 09:00 to 11:00
Friday, January 12, 2018 - 09:00 to 11:00
Thursday, January 18, 2018 - 09:00 to 11:00

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