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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let Ω be a curvilinear polygon and QΩγ be the Laplacian in L2(Ω), QΩγÏ=âÎÏ, with the Robin boundary condition âνÏ=γÏ, where âν 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 âΩ. 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
Journal: Journal of Mathematical Analysis and Applications - Volume 461, Issue 2, 15 May 2018, Pages 1498-1543
نویسندگان
Magda Khalile,