This is my solution:
My approach was fairly simple:
1. Note down the possible digits for each cell, according to the rules.
2. Solve it like a usual Sudoku.
Here are the basic steps:
Put all the possible digits in the outlined areas according to the question:
Digits that appear multiple times inside one area and therefore have to must exist at a specific position:
Following the general Sudoku rules (specificly: unique digits in column, row and subgrids):
Some more deduction using the general Sudoku rules:
Continue to solve the Sudoku.