Two Symmetry Problems in Potential Theory
نویسنده
چکیده
The method of proof combines the Maximum Principles and the device (which goes back to A. D. Alexandroff: every embedded surface in R with constant mean curvature must be a sphere) of moving planes to a critical position and then showing that the solution is symmetric about the limiting plane. In a subsequent article, H. F. Weinberger [3] gave a simplified proof for the special case of the Poisson differential equation, ∆u = −1. Our aim at present is to introduce some variants on Serrin’s result and arrive at the same symmetry conclusions by employing elementary arguments. The next statement involves radial dependence on the boundary conditions.
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