On the Tricomi problem with a nonlocal conjugation condition for equations of mixed type (Q1593887)

The mixed type equation \[ \text{sgn }y|y|^m u_{xx}+ u_{yy}= 0,\tag{1} \] where \(m>0\), is considered in the domain \(D\) by a piecewise smooth curve \(\Gamma\), when \(y> 0\), with the ends in the points \(A(0,0)\) and \(B(1,0)\) and by the characteristics of (1), when \(y>0\), outcoming from \(A\) and \(B\). For (1) the generalization of the Tricomi problem with nonlocal conditions on the line \(y=0\) is considered. Correctness of this problem is proved.