Sumários
Lesson no. 7: The Laplace equation, part VI. The Heat equation, part I
15 Março 2019, 12:00 • Hugo Tavares
Poisson equation: The Dirichlet principle. Counterexample by Weierstrass on the existence of a minimizer. The heat/diffusion equation: initial and boundary conditions. The parabolic cylinder and the space of C^{2,1}-functions. The weak maximum principle and its consequences: uniqueness, stability and comparison principle.
Solution to exercise 3 of Exercise Sheet 2.
Lesson no. 6: The Laplace Equation, part V
12 Março 2019, 10:30 • Hugo Tavares
Green's function and Poisson's equation for the ball.
Consequences: Harnack's inequality.
Lesson no. 5: The Laplace equation, part IV
8 Março 2019, 12:00 • Hugo Tavares
Comments about the uniqueness of solution to the Poisson equation in the whole space: asymptotic behavior at infinity.
Green's function and representation formula. Example: the case of the ball in dimension 3 or higher.