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New bounds for the principal Dirichlet eigenvalue of planar regions. (English) Zbl 1180.35388

Summary: We present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Based on this, we propose new types of bounds and establish several conjectures regarding the dependence of this eigenvalue on the perimeter and the area.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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