Interpolating between torsional rigidity and principal frequency |
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| Authors: | Tom Carroll |
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| Affiliation: | a University College Cork, Ireland
b University of Cape Town, South Africa |
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| Abstract: | A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter. |
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| Keywords: | Torsional rigidity Principal frequency Sobolev embedding Semilinear partial differential equations |
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