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On a counterexample to a conjecture of Saint Venant

โœ Scribed by Mythily Ramaswamy

Publisher
Springer Netherlands
Year
1992
Tongue
English
Weight
281 KB
Volume
27
Category
Article
ISSN
0374-3535

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โœฆ Synopsis

The Saint Venant's conjecture for convex plane domains f~, having symmetry about two orthogonal axes, is that the maximum of [Vu[ occurs only at the points on df~ which are nearest to the origin. G. Sweers constructed one such domain f~ and claimed that either the conjecture fails for f~ or for f~ = {(x, y) ~ f~; u(x, y) > ~}, which again is convex. We give a totally different proof of this claim. Our proof brings out clearly the reason for the failure of the conjecture and also allows us to construct many more such domains.

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