Dimension ≥ 2: The “Simple” Cases: Abstract or Periodic Settings

The main tools we have used in the first chapter were weak convergence and average of functions. In the second chapter, differential operators came into play. We are now going to see that geometry is important (of course in dimensions higher than 2). We will also need to introduce some abstract arguments, hence in particular functional analysis. In these higher dimensions, we indeed cannot integrate analytically partial differential equations.