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[Community Question] Calculus: The dirichlet and harmonic functions why they are important

One of our user asked:

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 !


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