О ФРЕДГОЛЬМОВОЙ РАЗРЕШИМОСТИ КРАЕВЫХ ЗАДАЧ ДЛЯ ВОЛНОВЫХ УРАВНЕНИЙ С ДАННЫМИ НА ВСЕЙ ГРАНИЦЕ

ON FREDHOLM SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR THE WAVE EQUATIONS WITH THE CONDITIONS ON THE ENTIRE BOUNDARY

In this paper, we study boundary value problems for the wave equation with conditions on the entire boundary and obtain sufficient conditions for Fredholm solvability of the problem in suitable spaces of functions. It turns out that these conditions depend on the properties of the geodesic flow.