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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel


CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2017: 0.86

Open Access
Online
ISSN
2299-3274
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Conformal Geometry and the Composite Membrane Problem

Sagun Chanillo
Published Online: 2013-01-04 | DOI: https://doi.org/10.2478/agms-2012-0002

Abstract

We show that a certain eigenvalue minimization problem in two dimensions for the Laplace operator in conformal classes is equivalent to the composite membrane problem. We again establish such a link in higher dimensions for eigenvalue problems stemming from the critical GJMS operators. New free boundary problems of unstable type arise in higher dimensions linked to the critical GJMS operator. In dimension four, the critical GJMS operator is exactly the Paneitz operator.

Keywords: Eigenvalue Minimization in Conformal classes; GJMS operators; Composite Membrane problem; Free Boundary Problems; Conformal Geometry; Paneitz operator

MSC: 35R35; 35J60; 35B65; 58J50

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About the article

Received: 2012-09-27

Accepted: 2012-12-13

Published Online: 2013-01-04


Citation Information: Analysis and Geometry in Metric Spaces, Volume 1, Pages 31–35, ISSN (Online) 2299-3274, DOI: https://doi.org/10.2478/agms-2012-0002.

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©2012 Versita Sp. z o.o.. This content is open access.

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