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Re: Laplce equation


Dear Nguyen Binh Minh,

I suggest the setup U[r,theta,phi]=R[r]T[theta]F[phi]

and

Expand[(Laplacian[U[r,theta,phi],Spherical[r,theta,phi]])*r^2/U[r,theta,phi]]

gives ordinary differential equations for

R[r],     T[theta], and F[phi].

Depending on the location of your demicircle depending on theta, you
solve the
boundary value  problem for F[phi],

see for instance page 99 equation (3.1.79) of

Mathematical Methods of Physics and Engineeering with
Mathematica, CRCPress, Tokyo 2003



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