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Analysis Seminar

Thursday, October 25, 2018 - 3:00pm

Lotfi Hermi

Florida International University

Location

University of Pennsylvania

DRL 4C8

By introducing geometric factors and physical parameters that lend themselves to the Payne interpretation in Weinstein fractional space, we prove new isoperimetric inequalities for the fundamental eigenvalue of the Dirichlet problem and relate it to ``relative torsional rigidity'' which will be introduced. We motivate, conjecture, and prove these isoperimetric inequalities. They generalize and improve classical sharp inequalities dating back to the works of Payne-Weinberger (1960), Payne-Rayner (1973), Kohler-Jobin (1972), and Chiti (1982). They can also be viewed as weighted forms of the classical Faber-Krahn and Kohler-Jobin inequalities. Numerical evidence will be provided for certain triangles.