Asymptotics of the solutions of some higher order elliptic equations in conical domains

For the equation $((-1)^mP(D_x,D_y)+D_y)u=f$, where $P$ is a homogeneous positive polynomial of degree $2m$, $x\in\mathbf R^2$ and $y\in\mathbf R^1$, the first boundary value problem is considered in a conical domain. The asymptotics of the solution at infinity is studied under the condition that the right side and the boundary functions asymptotically coincide with polynomials.
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