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تسجيل مستخدم جديدالحلول التقريبية لمشكلة ديريشل لخرائط الهارمونية بين المساحات الهيبروبولية
Approximate solutions to the Dirichlet problem for harmonic maps between hyperbolic spaces
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نتيجتنا الرئيسية في هذا البحث هي التالية: بفرض $H^m, H^n$ هي مساحات هيبروليكية للأبعاد $m$ و $n$ المتطابقة، وبفرض دالة Holder $f=(s^1,...,f^{n-1}):partial H^mto partial H^n$ بين الحدود الهندسية لـ $H^m$ و $H^n$. ثم لكل $epsilon >0$ يوجد خريطة هارمونية $u:H^mto H^n$ التي تكون متواصلة حتى الحدود (بالأحوال الإيوكليدية) و $u|_{partial H^m}=(f^1,...,f^{n-1},epsilon)$.
Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic spaces of dimensional $m$ and $n$ corresponding, and given a Holder function $f=(s^1,...,f^{n-1}):partial H^mto partial H^n$ between geometric boundaries of $H^m$ and $H^n$. Then for each $epsilon >0$ there exists a harmonic map $u:H^mto H^n$ which is continuous up to the boundary (in the sense of Euclidean) and $u|_{partial H^m}=(f^1,...,f^{n-1},epsilon)$.
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