Abstract:
There are investigated elliptic pseudodifferential operators p(x,D)p(x,D) which are degenerate on a submanifold ΓΓ of any codimension. Under certain further assumptions, for the operator which is obtained by adjoining to p(x,D)p(x,D) boundary and coboundary conditions on the submanifold ΓΓ, there are constructed left and right regularizers, and theorems on hypoellipticity and local solvability are proved. In case p(x,D)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.
\Bibitem{Gru71}
\by V.~V.~Grushin
\paper On a~class of elliptic pseudodifferential operators degenerate on a~submani\-fold
\jour Math. USSR-Sb.
\yr 1971
\vol 13
\issue 2
\pages 155--185
\mathnet{http://mi.mathnet.ru/eng/sm3054}
\crossref{https://doi.org/10.1070/SM1971v013n02ABEH001033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=283630}
\zmath{https://zbmath.org/?q=an:0215.49203|0238.47038}
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https://www.mathnet.ru/eng/sm3054
https://doi.org/10.1070/SM1971v013n02ABEH001033
https://www.mathnet.ru/eng/sm/v126/i2/p163
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