The Theorem on Existence and Uniqueness of the Solution of One Boundary Value Problem in Strip for Degenerate Elliptic Equations of Higher Order

Abstract

Доказана теорема о существовании и единственности решения краевой задачи в полосе для одного вырождающегося эллиптического уравнения высокого порядка, вырождающегося на одной из границ полосы в уравнение третьего порядка по одной из переменных. Ключевые слова: априорная оценка, вырождающееся эллиптическое уравнение, весовые пространства С. Л. Соболева.

A Priori Estimate of Solutions of One Boundary-Value Problem in a Strip for a Higher-Order Degenerate Elliptic Equation

“…In this paper, we obtain a priori estimates for solutions of boundary-value problems in a strip for high-order equations that degenerate on the boundary into an equation of odd order in one of the variables. Thus, this work is a natural continuation of the research begun in [4,5,8]. The formulation of the obtained results is contained in [6].…”

“…In particular, boundary-value problems in a strip were studied for high-order equations that degenerate into an even-order equation on the boundary of the domain. In [4,5], A. D. Baev and S. S. Buneev studied boundary-value problems in a strip for high-order elliptic equations degenerating into a third-order equation. In [8], coercive a priori estimates were obtained for a high-order elliptic equation that degenerates into an equation of odd order at the boundary t = 0.…”