I want to solve the Laplace equation with drichlet boundary condition on 4 circles with radius $a$ in 2d plane. Circles are located at $x=r=0$, $x=y=A$, $x=A,y=0$ and $y=B, x=0$ and they do not overlap. I'm wondering if there is a way to do a conformal mapping for this system to make it easier to solve the Laplace equation. In the case of two circles, I know that it is possible to map the system to two concentric circles. Can somebody please help me?
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Poorly phrased, we don't even know if the circles overlap. And what is "the system" that you map ? – Nov 15 '19 at 16:10
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I'm editing it @YvesDaoust – Marco Nov 15 '19 at 16:11
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Is it fine now? @YvesDaoust – Marco Nov 15 '19 at 16:35
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Are you serious ? You changed two words. – Nov 15 '19 at 16:50
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What do you want to accomplish with your conformal mapping? – Sten Nov 15 '19 at 17:00
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I want to solve the Laplace equation between these 4 circles and I want to do the conformal mapping to get an easier geometry in which I can solve the Laplace equation @Sten – Marco Nov 15 '19 at 17:10
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1A conformal mapping is just one which locally preserves angles. So your question is really unclear. If you know something about the geometry (before and after the mapping), you could start by drawing a sketch, both for your sake and for ours – Sten Nov 15 '19 at 17:20
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Is it fine now? @YvesDaoust – Marco Nov 16 '19 at 00:51
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I tried to improve the question @Sten – Marco Nov 16 '19 at 00:52
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Are you serious ? You changed two words. – Nov 16 '19 at 13:49