Quantitative Estimates on Jacobians for Hybrid Inverse Problems
Keywords:
эллиптические уравнения, операторы Бельтрами, гибридные обратные задачи, композитные материалы.Abstract
Рассматриваются sigma-гармонические отображения, то есть отображения U с компонентами u_i, являющимися решениями эллиптического уравнения sigma nabla u_i=0, для i=1,... ,n. Исследуется вопрос нахождения таких условий Дирихле, при которых Якобиан отделен от нуля. Результаты такого рода необходимы при решении так называемых гибридных обратных задач, а также в теории усреднения границ для эффективных свойств композиционных материалов.References
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