A CLASS OF DEGENERATE ELLIPTIC OPERATORS
Andrei Vladimirovich Fursikov · Mathematics of the USSR-Sbornik · 1969
In a bounded region we consider an operator which is elliptic inside the region and degenerate on its boundary . More precisely, the operator has the following form in the local coordinate system , in which the boundary is given by the equation and for points in the region : where is a parameter, and for The operator will be proved Noetherian in certain spaces under the condition that is sufficiently large. In addition, some results will be obtained relating to how the smoothness of the solution of the equation depends on the magnitude of the parameter.A theorem is formulated concerning unique solvability in appropriate spaces for a class of degenerate parabolic operators.Bibliography: 8 items.