کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665422 1633814 2015 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On ratios of harmonic functions
ترجمه فارسی عنوان
بر روی نسبت توابع هارمونیک
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

Let u and v   be harmonic functions in Ω⊂RnΩ⊂Rn with the same zero set Z. We show that the ratio f   of such functions is always well-defined and is real analytic. Moreover it satisfies the maximum and minimum principles. For n=3n=3 we also prove the Harnack inequality and the gradient estimate for the ratios of harmonic functions, namely supK⁡|f|≤CinfK⁡|f|&supK⁡|∇f|≤CinfK⁡|f| for any compact subset K of Ω, where the constant C depends on K, Z, Ω   only. In dimension two the first inequality follows from the boundary Harnack principle and the second from the gradient estimate recently obtained by Mangoubi. It is an open question whether these inequalities remain true in higher dimensions (n≥4n≥4).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 274, 9 April 2015, Pages 241–262
نویسندگان
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