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 Nov 26 awarded Popular Question Dec 16 awarded Caucus Aug 28 awarded Benefactor Aug 28 accepted Solving the 2D Poisson equation with variable boundary location Aug 28 comment Solving the 2D Poisson equation with variable boundary location Wow, Awesome, thanks! Minor correction, you missed a minus sign in $A_1$ i.e. $A_1=\frac{C}{4}\frac{b^2-a^2}{a^2+b^2}$ Aug 28 comment Solving the 2D Poisson equation with variable boundary location I do see that they indeed use the elliptic coordinates that @rajb245 mentioned so that seems to be the right route Aug 28 comment Solving the 2D Poisson equation with variable boundary location @Semiclassical I can access the paper behind the paywall, but to be honest I don't exactly get what I am looking at. Aug 26 comment Solving the 2D Poisson equation with variable boundary location @rajb245 Ah, ok. Didn't know that coordinate system. I'm curious how it goes! Aug 25 comment Solving the 2D Poisson equation with variable boundary location @rajb245 Terrific thanks. Note that the bottom part of my question contains a transformation of (1) to (what I would call) elliptical coordinates. Might save you some work?! Aug 25 comment Solving the 2D Poisson equation with variable boundary location @Semiclassical Yes, that is indeed what I am looking for. Aug 24 awarded Promoter Aug 21 revised Solving the 2D Poisson equation with variable boundary location added 35 characters in body Aug 20 revised Solving the 2D Poisson equation with variable boundary location added some work Aug 20 comment Transforming the Laplace operator from Polar to Cartesian coordinates @BeniBogosel Isn't the mixed derivative supposed to have a factor 2? Aug 19 comment Solving the 2D Poisson equation with variable boundary location @Dmoreno ok, I think I get it now. Thanks! I actually know roughly what the solution to this problem should look like (because of the physical shape it represents) and I know that there isn't a singularity at $r=0$, but I will work with the mathematically correct formulation you propose! Aug 19 comment Solving the 2D Poisson equation with variable boundary location @Dmoreno I will certainly try the other choice of coordinates, indeed that would turn the boundary condition simply into $r=r_0=1$. I'm not sure I completely understand your second point, I can see that $r=0$ is indeed a singular point in the differential equation, but would the boundary condition be something like $\lim_{r\to0}$ $z_r\to0$ (sorry about the notation, don't quite know how to write that) ? Aug 19 revised Solving the 2D Poisson equation with variable boundary location better info in title Aug 19 asked Solving the 2D Poisson equation with variable boundary location Aug 14 comment Are there any surfaces that contain both positive and negative Gaussian curvature? Could you clarify what you mean with k1 and k2?! --- And just to clarify my own wording: with inside I mean at the side of the torus inside the hole, I do not mean actually inside the 'tube' of the torus Aug 7 comment What is this semicircle-like shape called? @Lucian Smiley?!