scholarly journals Faber-Krahn and Lieb-type inequalities for the composite membrane problem

2019 ◽  
Vol 18 (5) ◽  
pp. 2679-2691
Author(s):  
Giovanni Cupini ◽  
◽  
Eugenio Vecchi ◽  
Keyword(s):  
Composite Membrane ◽  
Membrane Problem

scholarly journals Conformal Geometry and the Composite Membrane Problem

2013 ◽  
Vol 1 ◽  
pp. 31-35 ◽  
Author(s):  
Sagun Chanillo
Keyword(s):  
Composite Membrane ◽  
Eigenvalue Problems ◽  
Free Boundary Problems ◽  
Conformal Geometry ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Boundary Problems ◽  
Paneitz Operator ◽  
Membrane Problem ◽  
The Laplace Operator

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.

scholarly journals Regularity of the minimizers in the composite membrane problem in R2

2008 ◽  
Vol 255 (9) ◽  
pp. 2299-2320 ◽  
Author(s):  
Sagun Chanillo ◽  
Carlos E. Kenig ◽  
Tung To
Keyword(s):  
Composite Membrane ◽  
Membrane Problem
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