Under what conditions should I use the methods of moving spheres instead of the method of mobile plans?
Under what conditions should I use the method of moving planes, but I can not use the method of moving spheres?
2026-03-27 07:14:57.1774595697
Method of Moving Planes and Method of Moving Spheres
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The method of moving spheres reflects across the sphere, using the Kelvin transformation, while the method of moving planes reflects across a plane.
For the Kelvin transform to be well defined, the domain of definition for the function needs to satisfy certain fairly specific properties, that is to say, $\frac{x}{|x|^2} \in \Omega$ for those $x \in \Omega$ where you want to do the comparison. Thus, it tends to be most useful on infinite domains that are "cones" of some kind or another, such as the upper half space.