A 2D boundary value problem with superelliptic boundaries

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kadir can erbas
kadir can erbas 2022-2-4
I have 2 concentric supercircles with equations x^4+y^4=1 and x^4+y^4=16. Potentials at these surfaces are kept constant at V=0 and V=1 respectively as shown in the figure. How can I solve the laplace equation for V in these boundary conditions?

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