A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains

作者：Hasnaoui Abdelhalim; Hermi Lotfi^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(5): 2419-2440.

DOI：10.1007/s00033-015-0530-1

• Fundamental eigenvalue
• Upper bound
• Isoperimetric Saint-Venant inequality
• Crooke-Sperb inequality
• Wedge-like membrane

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.

• 出版日期2015-10