Geodesic
Conformal Geometry and the Composite Membrane Problem
Analysis and Geometry in Metric Spaces, Tome 1 (2013) no. 1, pp. 31-35 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : Eigenvalue Minimization in Conformal classes, GJMS operators, Composite Membrane problem, Free Boundary Problems, Conformal Geometry, Paneitz operator 
@article{AGMS_2013_1_1_a1,
     author = {Chanillo, Sagun},
     title = {Conformal {Geometry} and the {Composite} {Membrane} {Problem}},
     journal = {Analysis and Geometry in Metric Spaces},
     pages = {31--35},
     year = {2013},
     volume = {1},
     number = {1},
     zbl = {1258.35209},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2013_1_1_a1/}
}
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Chanillo, Sagun. Conformal Geometry and the Composite Membrane Problem. Analysis and Geometry in Metric Spaces, Tome 1 (2013) no. 1, pp. 31-35. http://geodesic.mathdoc.fr/item/AGMS_2013_1_1_a1/