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Bounds for the first eigenvalue of the elastically supported membrane on convex domains

by R. Sperb

(Report number 2003-03)

Abstract
Barta's principle and gradient boudns for the torsion function are the main tools for deriving lower bounds for the first eigenvalue. The optimal domains are an infinite strip, a disk or an annulus in different situations.

Keywords: Eigenvalues of the Laplacian, Robin boundary conditions

@Techreport{S03_315,
  author = {R. Sperb},
  title = {Bounds for the first eigenvalue of the elastically supported membrane on convex domains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-03.pdf },
  year = {2003}
}

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