Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions

Catherine Bandle; Alfred Wagner

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arXiv · 1403.3249

Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions

Catherine Bandle·Alfred Wagner

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Abstract

An inequality for the reverse Bossel-Daners inequality is derived by means of the harmonic transplantation and the first shape derivative. This method is then applied to elliptic boundary value problems with inhomogeneous Neumann conditions. The first variation is computed and an isoperimetric inequality is derived for the minimal energy.

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Catherine Bandle, Alfred Wagner. 2014-03-13. Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions. https://arxiv.org/abs/1403.3249

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