Partial Differential Equations (PDE) are relevant in nearly all fields of mathematics and in the sciences in general.
Among the many relevant questions are existence, uniqueness, regularity, and stability of solutions of PDE.
A famous still open problem is the existence and smoothness of solutions to the Navier–Stokes equations, named as one of the Millennium Prize Problems in 2000.
PDE are foundational in the scientific understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics.
PDE also arise in mathematical considerations, such as differential geometry and the calculus of variations. Among other notable applications, they are the fundamental tool in the proof of the Poincaré conjecture from geometric topology.
In this lecture the basic mathematical theory for PDE will be given.
- Lehrende/r: André Schlichting