Influence of lower order pseudodifferential terms on the solvability of degenerate elliptic equations (Q810284)

The author considers some examples of degenerate pseudodifferential equations arising in particular from the oblique derivative problem for harmonic functions in half-space. Since the principal symbol of the pseudodifferential equation \(Pu=f\) degenerates at some set, then its solvability properties depend also on its lower order terms. The simplest example is the following elliptic equation \[ x^ 2u_{yy}+(x^ 2+b^ 2)u_{xx}+b\quad Ju=f, \] with degeneration on \(x=0\), where Ju is an operator of order less than two.