کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899670 1631550 2018 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian
چکیده انگلیسی
In this paper we study integral estimates of derivatives of conformal mappings φ:D→Ω of the unit disc D⊂C onto bounded domains Ω that satisfy the Ahlfors condition. These integral estimates lead to estimates of constants in Sobolev-Poincaré inequalities, and by the Rayleigh quotient we obtain spectral estimates of the Neumann-Laplace operator in non-Lipschitz domains (quasidiscs) in terms of the (quasi)conformal geometry of the domains. Specifically, the lower estimates of the first non-trivial eigenvalues of the Neumann-Laplace operator in some fractal type domains (snowflakes) were obtained.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 463, Issue 1, 1 July 2018, Pages 19-39
نویسندگان
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