2017
Том 69
№ 9

Всі номери

О краевых задачах для эллиптического уравнения с комплексными коэффициекгами и одной проблеме моментов

Бурський В. П.

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Абстракт

The elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of the solution are obtained for an arbitrary bounded region with a smooth boundary. These conditions are formulated in terms of a certain moment problem on the boundary of the region; they are applied to the study boundary-value problems. In particular, it is shown that the Dirichlet and Neumann problems are solvable only together. The above-mentioned moment problem is solved, together with the Dirichlet problem and the Neumann problem, in the case where the region is a disk. The third boundary-value problem on a disk is also investigated.

Англомовна версія (Springer): Ukrainian Mathematical Journal 45 (1993), no. 11, pp 1659-1668.

Зразок цитування: Бурський В. П. О краевых задачах для эллиптического уравнения с комплексными коэффициекгами и одной проблеме моментов // Укр. мат. журн. - 1993. - 45, № 11. - С. 1476–1483.

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