Conformal Geometry and the Composite Membrane Problem

• Autorzy: Sagun Chanillo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 58J50: Spectral problems; spectral geometry; scattering theory
• 35R35: Free boundary problems
• 35J60: Nonlinear elliptic equations
• 35B65: Smoothness and regularity of solutions

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 31-35

Daty

otrzymano

2012-09-27

zaakceptowano

2012-12-13

online

2013-01-04

Twórcy

autor

Sagun Chanillo

• Department of Mathematics, Rutgers University,
  110 Frelinghuysen Rd., Piscataway, NJ 08854, U.S.A.

Bibliografia

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• Chanillo, S., Grieser, D., and Kurata, K.: The Free Boundary in the Optimization of Composite Membranes, Contemporary Math. of the AMS 268 (2000), 61-81.
• Chanillo, S., and Kenig, C.: Weak Uniqueness and Partial Regularity in the Composite Membrane problem, J. European Math. Soc. 10 (2008), 705-737.
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Identyfikatory

DOI

10.2478/agms-2012-0002