A class of higher-order elliptic equations degenerate on a portion of the boundary (Q1109960)

The author considers the equation \[ A(x,y,D_ x,D_ y)u(x,y)=f(x,y),\quad (x,y)\in G\subset R^ 2, \] where A is an elliptic differential operator (with complex coefficients) of order 2m degenerating on a part of \(\partial G\); the domain G is bounded by the segment \([x_ 1,x_ 2]\) on the x-axis and a curve connecting the points \((x_ 1,0)\), \((x_ 2,0)\) and laying in the upper half-plane. General boundary value problems are investigated including the classical problems of Tricomi, Gellerstedt and Chapligin. Coercive estimates for the strong solutions are obtained and theorems of existence are proved.