New Method of Solvability of a Three-dimensional Laplace Equation with Nonlocal Boundary Conditions
DOI:
https://doi.org/10.15407/mag12.03.185Анотація
Вивчено розв'язки крайової задачi з нелокальними граничними умовами для тривимiрного рiвняння Лапласа. Тут граничнi умови є найбiльш поширеними i лiнiйними. Вiдзначимо, що сингулярнi iнтеграли, що входять до необхiдних умов, є багатовимiрними. Таким чином, регуляризацiя цих особливостей незрiвнянно складнiша за регуляризацiю одновимiрних сингулярних iнтегралiв. Пiсля регуляризацiї сингулярностей доведено фредгольмовiсть поставленої задачi.
Mathematical Subject Classification: 35J05, 35J40.
Ключові слова:
нелокальні граничні умови, тривимірне рівняння Лапласа, багатовимірний сингулярний інтеграл, необхідні умови, регуляризація, фредгольмовістьПосилання
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