کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4610201 1338550 2015 47 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Asymptotic expansion of the trace of the heat kernel associated to the Dirichlet-to-Neumann operator
چکیده انگلیسی

For a given bounded domain Ω with smooth boundary in a smooth Riemannian manifold (M,g)(M,g), by decomposing the Dirichlet-to-Neumann operator into a sum of the square root of the Laplacian and a pseudodifferential operator, and by applying Grubb's method of symbolic calculus for the corresponding pseudodifferential heat kernel operators, we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to Dirichlet-to-Neumann operator as t→0+t→0+. In particular, we explicitly give the first four coefficients of this asymptotic expansion. These coefficients provide precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the Steklov problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 259, Issue 7, 5 October 2015, Pages 2499–2545
نویسندگان
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