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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

IMPACT FACTOR 2018: 0.536

CiteScore 2018: 0.83

SCImago Journal Rank (SJR) 2018: 1.041
Source Normalized Impact per Paper (SNIP) 2018: 0.801

Mathematical Citation Quotient (MCQ) 2017: 0.86

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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


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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