کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4618144 1339399 2012 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Laplace eigenvalues on regular polygons: A series in 1/N
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Laplace eigenvalues on regular polygons: A series in 1/N
چکیده انگلیسی

For regular polygons PN inscribed in a circle, the eigenvalues of the Laplacian converge as N→∞ to the known eigenvalues on a circle. We compute the leading terms of λN/λ in a series in powers of 1/N, by applying the calculus of moving surfaces to a piecewise smooth evolution from the circle to the polygon. The O(1/N2) term comes from Hadamardʼs formula, and reflects the change in area. This term disappears if we “transcribe” the polygon, scaling it to have the same area as the circle.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 385, Issue 1, 1 January 2012, Pages 135-149