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September  2017, 16(5): 1843-1859. doi: 10.3934/cpaa.2017089

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

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

Received  November 2016 Revised  January 2017 Published  May 2017

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.

Citation: Monika Laskawy. Optimality conditions of the first eigenvalue of a fourth order Steklov problem. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1843-1859. doi: 10.3934/cpaa.2017089
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