کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899944 1631553 2018 46 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectral asymptotics for Robin Laplacians on polygonal domains
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Spectral asymptotics for Robin Laplacians on polygonal domains
چکیده انگلیسی
Let Ω be a curvilinear polygon and QΩγ be the Laplacian in L2(Ω), QΩγψ=−Δψ, with the Robin boundary condition ∂νψ=γψ, where ∂ν is the outer normal derivative and γ>0. We are interested in the behavior of the eigenvalues of QΩγ as γ becomes large. We prove that the asymptotics of the first eigenvalues of QγΩ is determined at the leading order by those of model operators associated with the vertices: the Robin Laplacians acting on the tangent sectors associated with ∂Ω. In the particular case of a polygon with straight edges the first eigenpairs are exponentially close to those of the model operators. Finally, we prove a Weyl asymptotics for the eigenvalue counting function of QΩγ for a threshold depending on γ, and show that the leading term is the same as for smooth domains.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 461, Issue 2, 15 May 2018, Pages 1498-1543
نویسندگان
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