Strict monotonicity and unique continuation for the third-order spectrum of biharmonic operator (Q1938240)
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scientific article; zbMATH DE number 6134116
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strict monotonicity and unique continuation for the third-order spectrum of biharmonic operator |
scientific article; zbMATH DE number 6134116 |
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Strict monotonicity and unique continuation for the third-order spectrum of biharmonic operator (English)
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4 February 2013
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Summary: We study the spectrum for the biharmonic operator involving the Laplacian and the gradient of the Laplacian with weight, which we call third-order spectrum. We show that the strict monotonicity of the eigenvalues of the operator \(\Delta^2 u + 2\beta \cdot \nabla(\Delta u) + |\beta|^2 \Delta u\), where \(\beta \in \mathbb R^N\), holds if some unique continuation property is satisfied by the corresponding eigenfunctions.
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