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On Positivity for the Biharmonic Operator under Steklov Boundary Conditions

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Abstract

The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy

    Filippo Gazzola

  2. Mathematisches Institut, Universität zu Köln, D 50923, Köln, Germany

    Guido Sweers

  3. Delft Institute of Applied Mathematics TUDelft, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Guido Sweers

Authors
  1. Filippo Gazzola
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  2. Guido Sweers
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Correspondence to Filippo Gazzola.

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Communicated by C.A. Stuart.

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Gazzola, F., Sweers, G. On Positivity for the Biharmonic Operator under Steklov Boundary Conditions. Arch Rational Mech Anal 188, 399–427 (2008). https://doi.org/10.1007/s00205-007-0090-4

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  • DOI: https://doi.org/10.1007/s00205-007-0090-4

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