On Friedrichs constant and Horgan-Payne angle for LBB condition

Monique Dauge, Christine Bernardi, Martin Costabel, and Vivette Girault

In dimension 2, the Horgan-Payne angle serves to construct a lower bound for the inf-sup constant of the divergence arising in the so-called LBB condition. This lower bound is equivalent to an upper bound for the Friedrichs constant. Explicit upper bounds for the latter constant can be found using a polar parametrization of the boundary. Revisiting carefully the original paper which establishes this strategy, we found out that some proofs need clarification, and some statements, replacement.

March 2013

Monografiás Matemáticas García de Galdeano 39, 87-100 (2014).

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