Abstract
В.Г. Николаев Новгородский государственный университет имени Ярослава Мудрого, Великий Новгород, Российская Федерация E-mail: vg14@inbox.ru. V.G. Nikolaev Federal State-Funded Educational Institution of Higher Vocational Education “Yaroslav-the-Wise Novgorod State University”, Velikiy Novgorod, Russian Federation E-mail: vg14@inbox.ru
Highlights
∂ fλ − λ ∂ fλ = 0, ∂y ∂x ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ λ -ɝɨɥɨɦɨɪɮɧɨɣ ɜ ɨɛɥɚɫɬɢ D. ȼ [1] ɩɨɤɚɡɚɧɨ, ɱɬɨ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɜ ɱɚɫɬɧɵɯ ɩɪɨɢɡɜɨɞɧɵɯ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ (1) ɹɜɥɹɟɬɫɹ ɷɥɥɢɩɬɢɱɟɫɤɨɣ
For these matrices the inhomogeneous Schwarz problem in case of any boundary function ȥ has the unique solution
Summary
Ɜɟɤɬɨɪ-ɮɭɧɤɰɢɹ φ = φ(z) ∈C1(D), ɞɥɹ ɤɨɬɨɪɨɣ ɜ ɨɛɥɚɫɬɢ D ⊂ R2 ɜɵɩɨɥɧɟɧɨ ɭɪɚɜɧɟɧɢɟ Ɂɡ (1) ɜɵɬɟɤɚɟɬ, ɱɬɨ J -ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɮɭɧɤɰɢɢ ɨɩɪɟɞɟɥɟɧɵ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɜɟɤɬɨɪ-ɩɨɫɬɨɹɧɧɨɣ. Ɍɨɝɞɚ ɪɚɡɪɟɲɢɦɨɫɬɶ ɡɚɞɚɱɢ ɒɜɚɪɰɚ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɣ ɝɪɚɧɢɱɧɨɣ 2 -ɜɟɤɬɨɪ-ɮɭɧɤɰɢɢ ψ ∈C(Γ) ɪɚɜɧɨɫɢɥɶɧɚ ɪɚɡɪɟɲɢɦɨɫɬɢ ɫɤɚɥɹɪɧɨɣ ɡɚɞɚɱɢ gμ + f λ + l ⋅ fλ |Γ = φ(t), fλ , gμ ∈C(D), l = det (x, y) ∈ C
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