Analytic continuation of solutions of homogeneous irregular elliptic higher-order equations in a plane (Q913087)

The author studies a homogeneous elliptic equation of order n with constant complex coefficients in a simply connected domain \({\mathcal D}\subset R^ 2\) with boundary \(\Gamma\). Let \(\gamma\) \(\subset \Gamma\) be a flat piece of the boundary. The author studies the possibility of analytic continuation of the solution across \(\gamma\). It is known that if the equation is properly elliptic and the first n/2 Cauchy data are analytic then the solution can be analytically continued across \(\gamma\). The author completely studies this question for elliptic equations not being properly elliptic. He studies both the cases of simple and multiple roots of the characteristic equation. The author also finds the minimal number of Cauchy-type conditions sufficient for the existence of analytic continuation. The formula of such analytic continuation is given.