Geodesic
On a~class of elliptic pseudodifferential operators degenerate on a~submani\-fold
Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 155-185

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There are investigated elliptic pseudodifferential operators $p(x,D)$ which are degenerate on a submanifold $\Gamma$ of any codimension. Under certain further assumptions, for the operator which is obtained by adjoining to $p(x,D)$ boundary and coboundary conditions on the submanifold $\Gamma$, there are constructed left and right regularizers, and theorems on hypoellipticity and local solvability are proved. In case $p(x,D)$ is defined on a smooth compact manifold it is shown to be noetherian on special weighted spaces of Sobolev type. Bibliography: 24 titles. 
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     author = {V. V. Grushin},
     title = {On a~class of elliptic pseudodifferential operators degenerate on a~submani\-fold},
     journal = {Sbornik. Mathematics},
     pages = {155--185},
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     volume = {13},
     number = {2},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_2_a0/}
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V. V. Grushin. On a~class of elliptic pseudodifferential operators degenerate on a~submani\-fold. Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 155-185. http://geodesic.mathdoc.fr/item/SM_1971_13_2_a0/