On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domain
Abstract
Let Ω ϲ R2 be a domain having a compact boundary Σ which is Lipschitz and piecewise C4 smooth, and let ѵ denote the inward unit normal vector on Σ. We study the principal eigenvalue E(β) of the Laplacian in Ω with the Robin boundary conditions მ(f)/∂(ѵ)+β(f)= 0 on Σ, where β is a positive number. Assuming that Σ has no convex corners, we show the estimate E(β ) =-β2-γmax +O(β⅔) as β→+ꚙ ,where γmax is the maximal curvature of the boundary.
Supporting agencies: The research was partially supported by ANR NOSEVOL and GDR Dynamique quantique.
About the Author
K. Pankrashkin
Laboratoire de mathematiques
France
France
Konstantin Pankrashkin
UMR 8628, Universite Paris-Sud, Batiment 425, 91405 Orsay Cedex
http://www.math.u-psud.fr/pankrash/
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Review
For citations:
Pankrashkin K. On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domain. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(4):474-483.
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