Dirichlet problem

Alright kiddo, imagine you have a puzzle with missing pieces. The Dirichlet problem is like trying to find out what the missing pieces are supposed to look like.

Let's say you have a puzzle of a picture and you know what the border of the puzzle looks like, but the inside pieces are missing. This is similar to the Dirichlet problem. Instead of a puzzle, we have a mathematical problem where we know what the values of a function are at the border of a shape, but we don't know what the values of the function are inside the shape.

For example, let's say we have a square and we know what the temperature is at the edges of the square. We can use the Dirichlet problem to figure out what the temperature is at any point inside the square, just like how we can use the puzzle pieces to fill in the picture.

So, the Dirichlet problem is all about figuring out what the missing pieces of a puzzle, or a mathematical function, look like when we know what the edges, or the borders, look like.