Chiti-type Reverse Hölder Inequality and Saint-Venant Theorem for Wedge Domains on Spheres

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Abdelhalim Hasnaoui, Abdelhamid Zaghdani


In this paper, we prove a new weighted reverse Hölder inequality for the first eigenfunction of the Dirichlet eigenvalue problem in a domain completely contained in a wedge in the sphere S2. This inequality is known as the Payne-Rayner inequality or Chiti-type inequality. We also prove an extension of Saint-Venant inequality for the relative torsional rigidity of such domains.

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