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.

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 functino space.The Laplace equation. Mean Value Theorem

Lesson no. 1: Introduction

19 Fevereiro 2019, 14:00 • Hugo Tavares

Presentation of the course: program, main references, grading policy and evaluation.

Classification of PDEs (Partial Differential Equations) in linear and nonlinear, and classification of nonlinear equations in semi-linear, quasi-linear, and fully nonlinear. Examples arising in physics, population dynamics and geometry. Survey about known facts: Lebesgue spaces, Holder inequality, Lebesgue's dominated convergence theorem.