Abstract
By introducing new geometric factors which lend themselves to the Payne interpretation in Weinstein fractional space, we prove new isoperimetric inequalities which complement those of Payne–Weinberger and Saint-Venant giving a new upper bound for the fundamental mode of vibration of a wedge-like membrane and a new lower bound for its “relative torsional rigidity”. We also prove a new weighted version of a result of Crooke–Sperb for the associated fundamental eigenfunction of the Dirichlet Laplacian for such domains. A new weighted Rellich-type identity for wedge-like domains is also proved to achieve this latter task.
Original language | English (US) |
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Pages (from-to) | 2419-2440 |
Number of pages | 22 |
Journal | Zeitschrift fur Angewandte Mathematik und Physik |
Volume | 66 |
Issue number | 5 |
DOIs | |
State | Published - Oct 1 2015 |
Keywords
- Crooke–Sperb inequality
- Fundamental eigenvalue
- Isoperimetric Saint-Venant inequality
- Upper bound
- Wedge-like membrane
ASJC Scopus subject areas
- General Mathematics
- General Physics and Astronomy
- Applied Mathematics