IJPAM: Volume 116, No. 2 (2017)

Title

THE VARIATION OF THE FIRST EIGENVALUE OF
THE LAPLACE OPERATOR AND THE PROBLEM
OF LOCATING AN OBSTACLE

Authors

Badahi Ould Mohamed
Department of Mathematics
Faculty of Science and Arts at Al Qurayat
Al-Jouf University
KINGDOM OF SAUDI ARABIA

Abstract

By using the derivation and variation of the first eigenvalue of the Laplace operator and the reflection properties we show that if $B$ is a obstacle that moves inside $\Omega$, then the first eigenvalue of the Laplace operator $\lambda_1 $, is minimal when the obstacle touches the boundary of the domain $\Omega$.

History

Received: 2017-01-28
Revised: 2017-07-30
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 46B55, 46C75, 82H10, 49M40
Key Words and Phrases: first eigenvalue, obstacle, translation, elliptic operator, the maximum principle, variation

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How to Cite?

DOI: 10.12732/ijpam.v116i2.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 361 - 372


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