Strict inequality of Robin eigenvalues for elliptic differential operators on Lipschitz domains |
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Authors: | Jonathan Rohleder |
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Affiliation: | Technische Universität Graz, Institut für Numerische Mathematik, Steyrergasse 30, 8010 Graz, Austria |
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Abstract: | On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions. We prove that inequality between these functions on the boundary implies strict inequality between the eigenvalues of the two operators, provided that the inequality of the functions in the boundary conditions is strict on an arbitrarily small nonempty, open set. |
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Keywords: | Eigenvalue inequality Elliptic differential operator Robin boundary condition |
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