On the Compactness of One Class of Solutions for the Dirichlet Problem
DOI:
https://doi.org/10.15407/mag20.01.082Анотація
Ми розглядаємо задачу Дiрiхле для рiвняння Бельтрамi у довiльнiй обмеженiй однозв’язнiй областi комплексної площини $\mathbb {C}$. Само, вивчається клас усiх регулярних розв’язкiв цiєї задачi з умовами нормування i теоретико-множинними обмеженнями на їх комплексну характеристику. Доведена компактнiсть цього класу в термiнах простих кiнцiв за наявностi довiльної неперервної функцiї в умовi Дiрiхле.
Mathematical Subject Classification 2020: 30C65, 35J70
Ключові слова:
рiвняння Бельтрамi, простi кiнцi, плоскi вiдображення зi скiнченним та обмеженим спотвореннямПосилання
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