Some boundary value problems for elliptic equations, and the Lie algebras connected with them. II

This article presents detailed results on solvability and regularity of solutions for the noncoercive boundary value problem $lu=f$ in $\Omega$, $Au=g$ on $\partial\Omega$, where $l$ is a second-order elliptic operator in a bounded region $\Omega\subset\mathbf R^{n+1}$, and $A$ is a second-order operator for which the Lopatinskii conditions are violated on a sufficiently arbitrary subset of $\partial\Omega$. In particular, the principal part of $A$ need not be of definite sign on $T^*(\partial\Omega)$, and this leads (with a view to obtaining well-posed formulations) to the additional condition $u=h$ on $\mu_1$ and to the allowance of a finite discontinuity of $u|_{\partial\Omega}$ on $\mu_2$, where $\mu_1$ and $\mu_2$ are submanifolds of $\partial\Omega$ of codimension 1. The paper encompasses a large part of the known results on the degenerate oblique derivative problem.
Bibliography: 10 titles.