Optimality conditions of the first eigenvalue of a fourth order Steklov problem

Monika Laskawy

doi:10.3934/cpaa.2017089

Article Contents

2017, Volume 16, Issue 5: 1843-1859. Doi: 10.3934/cpaa.2017089

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Optimality conditions of the first eigenvalue of a fourth order Steklov problem

Monika Laskawy^,

Institut für Mathematik, RWTH Aachen, Templergraben 55, D-52062 Aachen, Germany

Received: November 2016

Revised: January 2017

Published: October 2017

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Abstract

In this paper we compute the first and second general domain variation of the first eigenvalue of a fourth order Steklov problem. We study optimality conditions for the ball among domains of given measure and among domains of given perimeter. We show that in both cases the ball is a local minimizer among all domains of equal measure and perimeter.

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Mathematics Subject Classification: 49K20, 49R05, 35N25, 65L15, 35J40.

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References

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