Jaime Arango, Adriana Gomez, Andres Salazar
Abstract:
In this article we investigate some qualitative properties of the solutions
of the classical linear model for clamped plates on circular domains,
under constant sign external loads. In particular we prove that inside
the circle there are at most a finite number of critical points,
which in turn rules out the existence of critical curves. We also study
the curvature of the level curves of the solutions, and we prove that
the curvature function is continuous up to the border, even though the
gradient of the solutions vanishes on the border circle.
Submitted August 26, 2014. Published October 16, 2014.
Math Subject Classifications: 35J40, 74K20.
Key Words: Clamped plates; critical points; curvature.
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Jaime Arango Universidad del Valle, Cali, Colombia email: jaime.arango@correounivalle.edu.co |
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Adriana Gómez Universidad del Valle, Cali, Colombia email: adriana.gomez@correounivalle.edu.co |
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Andrés Salazar Universidad Javeriana-Cali, Cali, Colombia. Universidad del Valle, Cali, Colombia email: andresmsalazar@javerianacali.edu.co |
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