Degenerate elliptic pseudodifferential equations of principal type

G. I. Èskin

Sbornik. Mathematics, Tome 11 (1970) no. 4, pp. 539-582

Résumé

This article studies pseudodifferential operators which are elliptic outside an $(n-1)$-dimensional submanifold $\omega$ of a closed $n$-dimensional manifold $\Gamma$. It is assumed that at those points of the cotangent bundle at which the ellipticity condition is violated the gradient of the determinant of the symbol is nonzero and transversal to $\omega$. On $\omega$ a number of boundary conditions are prescribed, and a number of potential operators with unknown densities are adjoined to the original equation; the normal solvability of this boundary value problem is then established. Bibliography: 21 titles.