I've already asked this question in a different thread but that fetched only luke warm response. Perhaps, my question was not very clear. I'm now starting this new thread after rephrasing my question so as to make my question clearer.
How many boundary conditions are needed to solve a 2nd order PDE in x and y ? For example, take the case of a 2D Laplace equation in x-y. It seems obvious that we need a total of 4 BC, 2 in x and 2 in y. But, what is confusing to me is the relation between the number of BC and the shape of the domain on which the PDE is to solved ? Text books always show the example of a rectangle domain which is pretty straight-forward. But, what if the domain is anything else arbitrary ? Will the number of BC be still 4 ?
Can you guys help me understand this ?
Thanks a lot in advance,