najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1189Research ArticleINVITED SPEAKERSINVITED SPEAKERSOn the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domainPankrashkinK.

Konstantin Pankrashkin

UMR 8628, Universite Paris-Sud,  Batiment 425, 91405 Orsay Cedex  http://www.math.u-psud.fr/pankrash/

konstantin.pankrashkin@math.u-psud.frLaboratoire de mathematiquesLaboratoire de mathematiques20132008202544Special Issue. INTERNATIONAL CONFERENCE "MATHEMATICAL CHALLENGE OF QUANTUM TRANSPORT IN NANOSYSTEMS - 2013. PIERRE DUCLOS WORKSHOP"474483Copyright © Pankrashkin K., 20252025Pankrashkin K.Pankrashkin K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1189

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.

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The authors declare that there are no conflicts of interest present.