Sumários

Lesson no. 4: The Laplace equation, part III

1 Março 2019, 12:00 Hugo Tavares

Local estimates for the gradient, Liouville Theorem.

The fundamental solution of the Laplace Equation. Solution of the Poisson equation in the whole space.


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28 Fevereiro 2019, 11:00 Hugo Tavares

Trabalho autónomo dos alunos.


Lesson no.3: The Laplace Equation, part II.

26 Fevereiro 2019, 14:00 Hugo Tavares

The weak and Strong maximum principles, and some of its consequences: uniqueness, stability and comparison results.

Energy methods: uniqueness of solution.Regularity theorem for harmonic function.
Solution to exercises 2 and 4(i)(ii)(iii) of Exercise Sheet 1.


Lesson no. 2. The transport Equation. The Laplace equation, part I

22 Fevereiro 2019, 12:00 Hugo Tavares

Equation for a general conservation law. Deduction of the Transport and Diffusion/Heat equations. 

The transport equation in the homogeneous and nonhomogeneous case: explicit solutions. Definition of weak solution using the test function space.The Laplace equation. Mean Value Theorem


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21 Fevereiro 2019, 11:00 Hugo Tavares

Trabalho autónomo dos alunos.