I am wondering why finding a function that is harmonic on the sphere and that respect some conditions on the frontiere of the sphere is important ?
This is called the Dirichlet problem, and I don't understand why we are interesting in this problem ?
Why are we want the function to be harmonic ?
I know what it means for a function to be harmonic, but I don't understand what is the "advantage" of being harmonic. Moreover does the solution of the Dircihlet helps solving real-life/physic problems ?
Thank you !